Distribution of end point distance for 2D self-avoiding and self-trapping walks of length n Hugo Pfoertner, December 5, 2002 http://www.pfoertner.org/ DIST: either Manhattan distance ...MAN |i_n| + |j_n| or squared Euclidean distance i_n^2 + j_n^2 SAW: all self-avoiding walks STW: all walks trapped after n steps (only for n>=7) #LENGTH OF WALK: 2 #IPATH: 3 ITRAP: 0 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 2 3 2 0 0 4 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 2.00000000 1.60947571 0.00000000 0.00000000 #ManhSums: 6 0 #SquarSums: 8 0 #LENGTH OF WALK: 3 #IPATH: 9 ITRAP: 0 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 1 2 2 0 0 3 7 0 0 0 5 0 6 0 0 9 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 2.55555556 2.04626754 0.00000000 0.00000000 #ManhSums: 23 0 #SquarSums: 41 0 #LENGTH OF WALK: 4 #IPATH: 25 ITRAP: 0 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 2 10 4 0 0 4 15 6 0 0 8 0 6 0 0 10 0 8 0 0 16 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 3.20000000 2.55702553 0.00000000 0.00000000 #ManhSums: 80 0 #SquarSums: 176 0 #LENGTH OF WALK: 5 #IPATH: 71 ITRAP: 0 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 1 6 6 0 0 3 34 0 0 0 5 31 22 0 0 9 0 12 0 0 13 0 20 0 0 17 0 10 0 0 25 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 3.70422535 2.95120531 0.00000000 0.00000000 #ManhSums: 263 0 #SquarSums: 679 0 #LENGTH OF WALK: 6 #IPATH: 195 ITRAP: 0 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 2 36 16 0 0 4 96 20 0 0 6 63 0 0 0 8 0 24 0 0 10 0 52 0 0 16 0 20 0 0 18 0 20 0 0 20 0 30 0 0 26 0 12 0 0 36 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 4.27692308 3.39052940 0.00000000 0.00000000 #ManhSums: 834 0 #SquarSums: 2452 0 #LENGTH OF WALK: 7 #IPATH: 543 ITRAP: 2 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 1 28 28 2 2 3 144 0 0 0 5 244 90 0 0 7 127 0 0 0 9 0 54 0 0 13 0 110 0 0 17 0 104 0 0 25 0 100 0 0 29 0 42 0 0 37 0 14 0 0 49 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 4.73112339 3.74768939 1.00000000 1.00000000 #ManhSums: 2569 2 #SquarSums: 8447 2 #LENGTH OF WALK: 8 #IPATH: 1479 ITRAP: 4 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 2 168 76 4 2 4 474 92 0 2 6 582 0 0 0 8 255 112 0 0 10 0 236 0 0 16 0 126 0 0 18 0 120 0 0 20 0 236 0 0 26 0 184 0 0 32 0 70 0 0 34 0 112 0 0 36 0 42 0 0 40 0 56 0 0 50 0 16 0 0 64 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 5.24949290 4.14988556 2.00000000 1.70710678 #ManhSums: 7764 8 #SquarSums: 28120 12 #LENGTH OF WALK: 9 #IPATH: 4067 ITRAP: 22 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 1 140 140 12 12 3 696 0 10 0 5 1386 440 0 8 7 1334 0 0 0 9 511 256 0 2 13 0 554 0 0 17 0 572 0 0 25 0 778 0 0 29 0 462 0 0 37 0 298 0 0 41 0 252 0 0 45 0 168 0 0 49 0 56 0 0 53 0 72 0 0 65 0 18 0 0 81 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 5.67863290 4.48714660 1.90909091 1.63129745 #ManhSums: 23095 42 #SquarSums: 91147 70 #LENGTH OF WALK: 10 #IPATH: 11025 ITRAP: 50 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 2 864 396 28 14 4 2418 468 22 14 6 3740 0 0 0 8 2980 568 0 8 10 1023 1196 0 12 16 0 654 0 2 18 0 660 0 0 20 0 1322 0 0 26 0 1272 0 0 32 0 560 0 0 34 0 1064 0 0 36 0 486 0 0 40 0 832 0 0 50 0 704 0 0 52 0 420 0 0 58 0 240 0 0 64 0 72 0 0 68 0 90 0 0 82 0 20 0 0 100 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 6.15963719 4.86101288 2.88000000 2.32747478 #ManhSums: 67910 144 #SquarSums: 289324 300 #LENGTH OF WALK: 11 #IPATH: 30073 ITRAP: 190 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 1 744 744 60 60 3 3654 0 84 0 5 7550 2314 46 62 7 9534 0 0 0 9 6544 1340 0 22 11 2047 0 0 0 13 0 2934 0 28 17 0 3064 0 16 25 0 4644 0 2 29 0 3000 0 0 37 0 2602 0 0 41 0 2352 0 0 45 0 2052 0 0 49 0 840 0 0 53 0 1398 0 0 61 0 924 0 0 65 0 1312 0 0 73 0 330 0 0 81 0 90 0 0 85 0 110 0 0 101 0 22 0 0 121 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 6.57091078 5.18425446 2.85263158 2.32400705 #ManhSums: 197607 542 #SquarSums: 902721 1254 #LENGTH OF WALK: 12 #IPATH: 81233 ITRAP: 456 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 2 4696 2164 148 72 4 13044 2532 214 76 6 21868 0 94 0 8 23328 3054 0 66 10 14202 6432 0 114 12 4095 0 0 0 16 0 3558 0 34 18 0 3644 0 28 20 0 7372 0 44 26 0 7424 0 20 32 0 3584 0 0 34 0 7020 0 0 36 0 3428 0 2 40 0 6420 0 0 50 0 7460 0 0 52 0 4728 0 0 58 0 3720 0 0 64 0 1364 0 0 68 0 2220 0 0 72 0 924 0 0 74 0 1584 0 0 80 0 990 0 0 82 0 904 0 0 90 0 440 0 0 100 0 110 0 0 104 0 132 0 0 122 0 24 0 0 144 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 7.02374651 5.53710275 3.76315789 2.99681476 #ManhSums: 570560 1716 #SquarSums: 2777112 4636 #LENGTH OF WALK: 13 #IPATH: 220375 ITRAP: 1504 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 1 4116 4116 300 300 3 20140 0 504 0 5 42120 12774 510 350 7 59842 0 190 0 9 55404 7366 0 154 11 30562 0 0 0 13 8191 16160 0 262 17 0 17036 0 198 25 0 26836 0 150 29 0 17846 0 64 37 0 17012 0 24 41 0 16256 0 0 45 0 15312 0 0 49 0 7072 0 2 53 0 12934 0 0 61 0 10428 0 0 65 0 17838 0 0 73 0 6380 0 0 81 0 2106 0 0 85 0 6798 0 0 89 0 2574 0 0 97 0 1430 0 0 101 0 1214 0 0 109 0 572 0 0 121 0 132 0 0 125 0 156 0 0 145 0 26 0 0 169 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 7.42067385 5.84902471 3.78457447 3.03210771 #ManhSums: 1635331 5692 #SquarSums: 8441319 16800 #LENGTH OF WALK: 14 #IPATH: 593611 ITRAP: 3720 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 2 26460 12240 738 348 4 73142 14220 1434 390 6 126862 0 1166 0 8 156670 17100 382 394 10 128742 36012 0 744 12 65352 0 0 0 14 16383 0 0 0 16 0 20030 0 296 18 0 20584 0 278 20 0 41882 0 492 26 0 43136 0 326 32 0 21652 0 100 34 0 43004 0 164 36 0 21260 0 70 40 0 41448 0 88 50 0 55340 0 28 52 0 35790 0 0 58 0 31916 0 0 64 0 13706 0 2 68 0 24604 0 0 72 0 11088 0 0 74 0 20724 0 0 80 0 16456 0 0 82 0 14832 0 0 90 0 10428 0 0 98 0 3432 0 0 100 0 9126 0 0 104 0 4912 0 0 106 0 4004 0 0 116 0 2002 0 0 122 0 1588 0 0 130 0 728 0 0 144 0 156 0 0 148 0 182 0 0 170 0 28 0 0 196 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 7.85198724 6.18560213 4.64086022 3.67683302 #ManhSums: 4661026 17264 #SquarSums: 25398500 57248 #LENGTH OF WALK: 15 #IPATH: 1604149 ITRAP: 11482 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 1 23504 23504 1576 1576 3 114758 0 2766 0 5 241178 72886 3780 1860 7 362408 0 2594 0 9 396134 41872 766 906 11 294348 0 0 0 13 139052 91916 0 1722 15 32767 0 0 0 17 0 97330 0 1520 25 0 156140 0 1650 29 0 105410 0 878 37 0 104602 0 510 41 0 103080 0 364 45 0 100168 0 252 49 0 48188 0 94 53 0 92136 0 116 61 0 82014 0 0 65 0 151730 0 32 73 0 63460 0 0 81 0 25124 0 2 85 0 89896 0 0 89 0 39468 0 0 97 0 28600 0 0 101 0 23882 0 0 109 0 16354 0 0 113 0 12870 0 0 117 0 10010 0 0 121 0 4466 0 0 125 0 12948 0 0 137 0 2730 0 0 145 0 2032 0 0 153 0 910 0 0 169 0 182 0 0 173 0 210 0 0 197 0 30 0 0 225 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 8.23660333 6.48781723 4.68785926 3.72836087 #ManhSums: 13212739 53826 #SquarSums: 75744301 192098 #LENGTH OF WALK: 16 #IPATH: 4311333 ITRAP: 28954 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 2 153188 71024 3796 1744 4 421774 82164 8500 2052 6 744440 0 9458 0 8 992444 98614 5666 2192 10 974492 207492 1534 4324 12 664790 0 0 0 14 294670 0 0 0 16 65535 115668 0 1984 18 0 119040 0 1928 20 0 242928 0 3644 26 0 253336 0 2958 32 0 129464 0 1176 34 0 259160 0 2114 36 0 129136 0 928 40 0 256696 0 1492 50 0 365128 0 1126 52 0 239916 0 616 58 0 225492 0 368 64 0 104020 0 122 68 0 195824 0 148 72 0 91872 0 0 74 0 176880 0 0 80 0 155804 0 0 82 0 147384 0 36 90 0 120492 0 0 98 0 48048 0 0 100 0 133656 0 2 104 0 76560 0 0 106 0 72072 0 0 116 0 47684 0 0 122 0 36972 0 0 128 0 12870 0 0 130 0 47632 0 0 136 0 16016 0 0 144 0 6210 0 0 146 0 8736 0 0 148 0 9548 0 0 160 0 3640 0 0 170 0 2552 0 0 178 0 1120 0 0 196 0 210 0 0 200 0 240 0 0 226 0 32 0 0 256 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 8.65068971 6.81131438 5.49174553 4.34038794 #ManhSums: 37296004 159008 #SquarSums: 224156984 622004 #LENGTH OF WALK: 17 #IPATH: 11616669 ITRAP: 85878 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 1 137412 137412 8584 8584 3 670330 0 15096 0 5 1410722 426238 24110 9996 7 2186266 0 22796 0 9 2625290 244092 12222 5100 11 2345974 0 3070 0 13 1487286 535830 0 10236 15 622318 0 0 0 17 131071 568482 0 9750 25 0 920852 0 12498 29 0 626790 0 7414 37 0 636390 0 5482 41 0 636320 0 4718 45 0 629292 0 3834 49 0 308644 0 1526 53 0 603818 0 2422 61 0 567550 0 1344 65 0 1085254 0 2078 73 0 489488 0 516 81 0 214178 0 154 85 0 799482 0 184 89 0 369688 0 0 97 0 306732 0 0 101 0 273944 0 40 109 0 219062 0 0 113 0 195910 0 0 117 0 170742 0 0 121 0 73328 0 2 125 0 253140 0 0 137 0 76622 0 0 145 0 103960 0 0 149 0 38896 0 0 153 0 36330 0 0 157 0 24752 0 0 169 0 20800 0 0 173 0 12830 0 0 185 0 4760 0 0 197 0 3154 0 0 205 0 1360 0 0 225 0 240 0 0 229 0 272 0 0 257 0 34 0 0 289 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 9.02469486 7.10516502 5.56326417 4.40756444 #ManhSums: 104836893 477762 #SquarSums: 658855781 1989798 #LENGTH OF WALK: 18 #IPATH: 31164683 ITRAP: 219516 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 2 905544 420436 20316 9138 4 2485586 485108 48854 11178 6 4428006 0 64616 0 8 6169898 581496 53454 12194 10 6748540 1222384 26134 24576 12 5552130 0 6142 0 14 3302424 0 0 0 16 1310412 681706 0 12084 18 262143 702212 0 11978 20 0 1435142 0 23370 26 0 1507116 0 21100 32 0 777820 0 9308 34 0 1564060 0 17582 36 0 783536 0 8168 40 0 1574104 0 14460 50 0 2319044 0 14670 52 0 1536758 0 9032 58 0 1486724 0 6652 64 0 709718 0 2404 68 0 1370800 0 3772 72 0 660672 0 1344 74 0 1291200 0 2328 80 0 1195508 0 1500 82 0 1157776 0 1518 90 0 1023548 0 700 98 0 444444 0 0 100 0 1274772 0 190 104 0 775328 0 224 106 0 747448 0 0 116 0 580970 0 0 122 0 487772 0 44 128 0 205920 0 0 130 0 768216 0 0 136 0 312832 0 0 144 0 118102 0 2 146 0 214032 0 0 148 0 202094 0 0 160 0 119168 0 0 162 0 48620 0 0 164 0 87516 0 0 170 0 144104 0 0 178 0 51920 0 0 180 0 37128 0 0 194 0 17136 0 0 196 0 11186 0 0 200 0 16896 0 0 212 0 6120 0 0 226 0 3844 0 0 234 0 1632 0 0 256 0 272 0 0 260 0 306 0 0 290 0 36 0 0 324 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 9.42447302 7.41774232 6.31580386 4.98444547 #ManhSums: 293710714 1386420 #SquarSums: 1924932324 6223140 #LENGTH OF WALK: 19 #IPATH: 83779155 ITRAP: 634294 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 1 818260 818260 48056 48056 3 3991598 0 83856 0 5 8398976 2540360 145742 55050 7 13255164 0 166016 0 9 16846672 1451238 122808 28806 11 16940838 0 55530 0 13 12963478 3184932 12286 59520 15 7287714 0 0 0 17 2752168 3381308 0 58874 19 524287 0 0 0 25 0 5506662 0 82422 29 0 3766096 0 51726 37 0 3876540 0 43758 41 0 3907626 0 40088 45 0 3905030 0 35592 49 0 1938602 0 15458 53 0 3842126 0 27038 61 0 3723536 0 19956 65 0 7252930 0 33004 73 0 3410612 0 11076 81 0 1571092 0 3646 85 0 6020698 0 10678 89 0 2865546 0 3828 97 0 2548056 0 2200 101 0 2376198 0 2046 109 0 2061746 0 924 113 0 1919060 0 0 117 0 1761552 0 0 121 0 795930 0 230 125 0 2911166 0 268 137 0 1060388 0 0 145 0 1671844 0 48 149 0 732836 0 0 153 0 644748 0 0 157 0 553384 0 0 169 0 534392 0 2 173 0 312404 0 0 181 0 184756 0 0 185 0 331228 0 0 193 0 100776 0 0 197 0 114042 0 0 205 0 126752 0 0 221 0 23256 0 0 225 0 14580 0 0 229 0 21862 0 0 241 0 7752 0 0 257 0 4628 0 0 265 0 1938 0 0 289 0 306 0 0 293 0 342 0 0 325 0 38 0 0 361 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 9.78922002 7.70429845 6.41069599 5.06737009 #ManhSums: 820132581 4066266 #SquarSums: 5593580859 19276694 #LENGTH OF WALK: 20 #IPATH: 224424291 ITRAP: 1636458 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 2 5441872 2528780 112194 49570 4 14903376 2913092 281094 62624 6 26680902 0 410406 0 8 38208834 3489180 412902 68916 10 44733440 7328512 277854 140506 12 41699706 0 117434 0 14 29941836 0 24574 0 16 15998964 4085684 0 71672 18 5766786 4210764 0 71980 20 1048575 8612324 0 142744 26 0 9080168 0 136334 32 0 4714142 0 63750 34 0 9505060 0 123550 36 0 4777646 0 59348 40 0 9659962 0 110534 50 0 14540168 0 131238 52 0 9681272 0 83540 58 0 9532632 0 69398 64 0 4645126 0 28036 68 0 9107156 0 48552 72 0 4458792 0 20940 74 0 8792136 0 38376 80 0 8378854 0 29164 82 0 8206260 0 26810 90 0 7588720 0 17762 98 0 3465396 0 5016 100 0 10098460 0 14192 104 0 6345364 0 8228 106 0 6191768 0 6028 116 0 5258572 0 3124 122 0 4690432 0 2690 128 0 2104960 0 0 130 0 8039516 0 1192 136 0 3530176 0 0 144 0 1445408 0 274 146 0 2761476 0 0 148 0 2612676 0 316 160 0 1869296 0 0 162 0 875160 0 0 164 0 1642472 0 0 170 0 2729872 0 52 178 0 1051340 0 0 180 0 947376 0 0 194 0 556512 0 0 196 0 278644 0 2 200 0 654328 0 0 202 0 335920 0 0 208 0 251940 0 0 212 0 265200 0 0 218 0 155040 0 0 226 0 158092 0 0 232 0 77520 0 0 234 0 99144 0 0 250 0 31008 0 0 256 0 18696 0 0 260 0 27852 0 0 272 0 9690 0 0 290 0 5512 0 0 298 0 2280 0 0 324 0 342 0 0 328 0 380 0 0 362 0 40 0 0 400 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 10.17682609 8.00755171 7.11671183 5.61106258 #ManhSums: 2283926980 11646200 #SquarSums: 16175728584 58797524 #LENGTH OF WALK: 21 #IPATH: 602201507 ITRAP: 4645024 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 1 4945292 4945292 275416 275416 3 24135878 0 475594 0 5 50747248 15370912 868430 310438 7 80979214 0 1106456 0 9 106740274 8764966 1001164 165156 11 115989096 0 621384 0 13 100992974 19229388 247430 346798 15 68550506 0 49150 0 17 34965672 20416954 0 350266 19 12058202 0 0 0 21 2097151 0 0 0 25 0 33350748 0 515672 29 0 22874936 0 333870 37 0 23746828 0 304558 41 0 24057862 0 288946 45 0 24199908 0 269286 49 0 12107608 0 123722 53 0 24189658 0 227754 61 0 23885788 0 188924 65 0 47075118 0 334620 73 0 22708724 0 130384 81 0 10784280 0 48884 85 0 41996750 0 168018 89 0 20344640 0 70928 97 0 18833982 0 49478 101 0 17983242 0 42198 109 0 16368360 0 27534 113 0 15607436 0 18876 117 0 14739270 0 14872 121 0 6890250 0 7618 125 0 25958270 0 20774 137 0 10507408 0 4316 145 0 17929100 0 3462 149 0 8258900 0 0 153 0 7509400 0 1508 157 0 6864576 0 0 169 0 7586790 0 322 173 0 4547194 0 368 181 0 3543956 0 0 185 0 6314872 0 0 193 0 2399244 0 0 197 0 2218004 0 56 205 0 3238308 0 0 221 0 1565904 0 0 225 0 999012 0 2 229 0 688470 0 0 233 0 406980 0 0 241 0 381786 0 0 245 0 232560 0 0 257 0 214892 0 0 261 0 108528 0 0 265 0 133152 0 0 281 0 40698 0 0 289 0 23630 0 0 293 0 34998 0 0 305 0 11970 0 0 325 0 6502 0 0 333 0 2660 0 0 361 0 380 0 0 365 0 420 0 0 401 0 42 0 0 441 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 10.53337595 8.28765230 7.23119622 5.70757033 #ManhSums: 6343214871 33589080 #SquarSums: 46572304083 177971680 #LENGTH OF WALK: 22 #IPATH: 1611140121 ITRAP: 12060586 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 2 33142948 15409308 635716 276662 4 90621310 17733640 1634504 359054 6 162652038 0 2533344 0 8 237076142 21231324 2882332 396388 10 290333166 44561704 2379364 813822 12 294691794 0 1377266 0 14 241344972 0 519758 0 16 155802806 24828282 98302 424294 18 76115282 25596288 0 429684 20 25165360 52371892 0 860138 22 4194303 0 0 0 26 0 55343956 0 848354 32 0 28839932 0 411104 34 0 58249040 0 808274 36 0 29339902 0 395168 40 0 59567472 0 758508 50 0 90907116 0 987106 52 0 60709752 0 638902 58 0 60459768 0 568948 64 0 29858042 0 248168 68 0 59093558 0 452582 72 0 29211680 0 206772 74 0 57928108 0 391246 80 0 56222124 0 327888 82 0 55457128 0 305900 90 0 52730584 0 236348 98 0 24840508 0 87912 100 0 73065024 0 244432 104 0 46793704 0 140084 106 0 46044996 0 126346 116 0 41209064 0 81108 122 0 38123556 0 64352 128 0 17714268 0 18876 130 0 68640316 0 75152 136 0 31413784 0 24024 144 0 13682038 0 10576 146 0 26570876 0 13468 148 0 25534898 0 16012 160 0 20339072 0 5824 162 0 9801792 0 0 164 0 18785000 0 0 170 0 32842272 0 4374 178 0 13625708 0 1876 180 0 12957060 0 0 194 0 8967296 0 0 196 0 4298798 0 374 200 0 11363272 0 424 202 0 6953544 0 0 208 0 5762320 0 0 212 0 5287646 0 0 218 0 4147320 0 0 226 0 3460364 0 60 232 0 2542656 0 0 234 0 2566884 0 0 242 0 705432 0 0 244 0 1293292 0 0 250 0 2293300 0 0 256 0 592978 0 2 260 0 1626820 0 0 272 0 538536 0 0 274 0 341088 0 0 290 0 287040 0 0 292 0 149226 0 0 298 0 175940 0 0 314 0 52668 0 0 324 0 29484 0 0 328 0 43440 0 0 340 0 14630 0 0 362 0 7604 0 0 370 0 3080 0 0 400 0 420 0 0 404 0 462 0 0 442 0 44 0 0 484 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 10.91044590 8.58280996 7.89666804 6.22169681 #ManhSums: 17578257134 95238444 #SquarSums: 133556779740 532719504 #LENGTH OF WALK: 23 #IPATH: 4316653453 ITRAP: 33801082 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 1 30255240 30255240 1610128 1610128 3 147778384 0 2749764 0 5 310427644 94158626 5178348 1787464 7 498778876 0 7076850 0 9 673654708 53619758 7303368 962300 11 771685650 0 5565732 0 13 735823552 117597458 3031244 2039220 15 570393470 0 1089042 0 17 351934006 124837492 196606 2086152 19 165105024 0 0 0 21 52428292 0 0 0 23 8388607 0 0 0 25 0 204265914 0 3167302 29 0 140354494 0 2089426 37 0 146500718 0 1992840 41 0 148910154 0 1933858 45 0 150432764 0 1853828 49 0 75650444 0 880258 53 0 151941806 0 1670900 61 0 151877458 0 1481296 65 0 301662890 0 2740208 73 0 147962664 0 1164238 81 0 71680232 0 479804 85 0 281990746 0 1746070 89 0 138154056 0 785300 97 0 131233026 0 617824 101 0 127153850 0 543030 109 0 119269650 0 414126 113 0 115487814 0 352924 117 0 111005704 0 301730 121 0 52950744 0 133738 125 0 203220192 0 443860 137 0 87722150 0 128856 145 0 157104196 0 166900 149 0 74241498 0 57772 153 0 69382508 0 60592 157 0 65277446 0 37492 169 0 79012066 0 33646 173 0 48742070 0 21582 181 0 41633748 0 0 185 0 76373200 0 7700 193 0 31863712 0 0 197 0 29174846 0 5438 205 0 47731928 0 2300 221 0 30390254 0 0 225 0 20323310 0 430 229 0 12564180 0 484 233 0 10323080 0 0 241 0 8527944 0 0 245 0 6972924 0 0 257 0 5265182 0 64 261 0 4005846 0 0 265 0 6568920 0 0 269 0 2288132 0 0 277 0 1634380 0 0 281 0 1916796 0 0 289 0 1818560 0 2 293 0 1387954 0 0 305 0 1236178 0 0 325 0 579360 0 0 333 0 229110 0 0 349 0 67298 0 0 361 0 36366 0 0 365 0 53326 0 0 377 0 17710 0 0 401 0 8824 0 0 409 0 3542 0 0 441 0 462 0 0 445 0 506 0 0 485 0 46 0 0 529 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 11.25965512 8.85713196 8.02715659 6.32949587 #ManhSums: 48604029143 271326578 #SquarSums: 381611332725 1584720770 #LENGTH OF WALK: 24 #IPATH: 11536599329 ITRAP: 88159110 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 2 204102568 94924584 3680972 1581616 4 557452870 109177984 9627838 2099356 6 1001812040 0 15500130 0 8 1477390320 130685432 19098924 2318314 10 1866052774 274133320 18091798 4781576 12 2010265604 0 12855630 0 14 1810292676 0 6633786 0 16 1335676450 152634118 2276818 2527948 18 790740444 157385192 393214 2573188 20 356985018 322072432 0 5181498 22 109051350 0 0 0 24 16777215 0 0 0 26 0 340802668 0 5213634 32 0 178019912 0 2584616 34 0 359951368 0 5126556 36 0 181551748 0 2531810 40 0 369607946 0 4952874 50 0 569294008 0 6819670 52 0 380950316 0 4461992 58 0 382281108 0 4143180 64 0 190499614 0 1895894 68 0 379410024 0 3567108 72 0 188745710 0 1679098 74 0 375708420 0 3237222 80 0 369111684 0 2877928 82 0 365870872 0 2742984 90 0 354309284 0 2307496 98 0 170327136 0 954338 100 0 504087854 0 2704644 104 0 326887114 0 1610170 106 0 323399060 0 1528250 116 0 299387116 0 1127324 122 0 283415396 0 932588 128 0 134672252 0 367796 130 0 526583896 0 1385582 136 0 247364024 0 542412 144 0 112087996 0 211128 146 0 219651416 0 362726 148 0 213442736 0 355188 160 0 181650972 0 198968 162 0 88635976 0 71500 164 0 171991552 0 129272 170 0 312148024 0 233158 178 0 136496856 0 86546 180 0 132203528 0 56784 194 0 101761488 0 26992 196 0 48890156 0 19096 200 0 135216328 0 28532 202 0 86292680 0 0 208 0 75703448 0 0 212 0 69592428 0 10000 218 0 60093504 0 0 226 0 50386960 0 6666 232 0 42380184 0 0 234 0 40980988 0 2784 242 0 15519504 0 0 244 0 29284472 0 0 250 0 50441048 0 0 256 0 11361650 0 490 260 0 38045616 0 548 272 0 13417116 0 0 274 0 11426448 0 0 288 0 2704156 0 0 290 0 12824888 0 68 292 0 6167172 0 0 296 0 3922512 0 0 298 0 5694700 0 0 306 0 2615008 0 0 314 0 2773848 0 0 320 0 1470942 0 0 324 0 1162556 0 2 328 0 1916704 0 0 338 0 692208 0 0 340 0 1016092 0 0 360 0 269192 0 0 362 0 489452 0 0 370 0 294448 0 0 386 0 85008 0 0 400 0 44390 0 0 404 0 64812 0 0 416 0 21252 0 0 442 0 10168 0 0 450 0 4048 0 0 484 0 506 0 0 488 0 552 0 0 530 0 48 0 0 576 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 11.62746963 9.14516037 8.65742578 6.81759615 #ManhSums: 134141458280 763230952 #SquarSums: 1086759598120 4674658232 #LENGTH OF WALK: 25 #IPATH: 30870338727 ITRAP: 244758534 #DIST SAWMAN SAWEUR2 STWMAN STWEUR2 1 187009888 187009888 9571864 9571864 3 914278594 0 16171420 0 5 1918838332 582751882 31076428 10479522 7 3096505988 0 44459014 0 9 4252787000 331526712 50106332 5691898 11 5055780450 0 43992540 0 13 5145677160 726889472 29393960 12126448 15 4397975762 0 14449812 0 17 3103494572 771411622 4750734 12508778 19 1768355870 0 786430 0 21 769588866 0 0 0 23 226491814 0 0 0 25 33554431 1263396502 0 19371160 29 0 869078054 0 12933200 37 0 910393320 0 12688180 41 0 927444230 0 12498220 45 0 939643656 0 12194478 49 0 474175350 0 5907676 53 0 955816362 0 11436254 61 0 963422270 0 10577700 65 0 1923787746 0 20097362 73 0 954383504 0 9010732 81 0 468691344 0 3951764 85 0 1856434992 0 14822572 89 0 916432992 0 6898032 97 0 885808374 0 5852270 101 0 866855382 0 5332608 109 0 829549208 0 4432528 113 0 811382698 0 4029190 117 0 789087002 0 3619550 121 0 381449340 0 1618598 125 0 1481956326 0 5777634 137 0 667091544 0 1994870 145 0 1232560136 0 3029348 149 0 591958850 0 1276314 153 0 563378418 0 1158274 157 0 539455746 0 944710 169 0 692739456 0 911910 173 0 436349046 0 542582 181 0 390811640 0 272272 185 0 733287804 0 523942 193 0 322396568 0 152048 197 0 300325210 0 194850 205 0 521788152 0 204738 221 0 381117298 0 36992 225 0 262887304 0 24958 229 0 162130798 0 37078 233 0 146306080 0 0 241 0 123375084 0 12784 245 0 110400108 0 0 257 0 84660482 0 8070 261 0 73632258 0 0 265 0 130834684 0 3332 269 0 55836364 0 0 277 0 44128260 0 0 281 0 42450408 0 0 289 0 48349034 0 554 293 0 31249856 0 616 305 0 38922176 0 0 313 0 10400600 0 0 317 0 8914800 0 0 325 0 27250794 0 72 333 0 8228610 0 0 337 0 4085950 0 0 349 0 3942246 0 0 353 0 2163150 0 0 361 0 1586464 0 2 365 0 2604522 0 0 373 0 961400 0 0 377 0 1363670 0 0 397 0 354200 0 0 401 0 626652 0 0 409 0 373934 0 0 425 0 106260 0 0 441 0 53676 0 0 445 0 78062 0 0 457 0 25300 0 0 485 0 11642 0 0 493 0 4600 0 0 529 0 552 0 0 533 0 600 0 0 577 0 50 0 0 625 0 1 0 0 Averages Manhattan all, SumSquares all, same trapped: 11.97004665 9.41426329 8.80103980 6.93476442 #ManhSums: 369519394643 2154129598 #SquarSums: 3085406711831 13719442862 