# Results of 1.2*10^10 simulated 2d STWs # ###################################### ########## # Moves, Trapped Failed Outmost visited # Count walks attempts Manhattan dist. Exact counts 0 0 21895586 0 ################################################### 1 0 53083102 0 All walks (A046661=A001411/4) 2 0 82343880 0 3 Self- 3 0 106136257 52831465 9 trapping 4 0 124771781 141909112 25 walks Probability of 5 0 139377619 238950504 71 occurrence Exact Simulation 6 0 151033363 319761222 195 A077482 A077483 A077484 7 32925028 160418775 386953259 543 1 2/(3^6 *2^0) 1/364.500 1/364.464 (=1.2*10^10/32925028) 8 27439839 168129319 437804089 1479 2 5/(3^7 *2^0) 1/437.400 1/437.320 9 56702039 174402297 474222226 4067 11 31/(3^8 *2^0) 1/211.645 1/211.633 10 52727311 179534993 497813713 11025 25 173/(3^9* 2^1) 1/227.549 1/227.586 11 77273704 183679439 510439511 30073 95 1521/(3^10*2^2) 1/155.290 1/155.292 12 71539169 186987000 513952551 81233 228 1056/(3^11*2^0) 1/167.753 1/167.740 13 94333778 189533871 510218494 220375 752 16709/(3^12*2^2) 1/127.223 1/127.208 14 86629244 191430161 500732911 593611 1860 184183/(3^13*2^4) 1/138.499 1/138.521 15 107424649 192707925 486798526 1604149 5741 1370009/(3^14*2^5) 1/111.718 1/111.706 16 99278729 193474834 469532085 4311333 14477 474809/(3^15*2^2) 1/120.882 1/120.872 17 117406703 193810680 449894233 11616669 42939 13478513/(3^16*2^5) 1/102.199 1/102.209 18 109163754 193675221 428750362 31164683 109758 150399317/(3^17*2^7) 1/109.907 1/109.927 19 125192756 193168884 406588870 83779155 317147 1034714947/(3^18*2^8) 1/ 95.852 1/ 95.852 20 116863363 192340643 383993357 224424291 818229 2897704261/(3^19*2*8) 1/102.681 1/102.684 21 131037679 191188241 361369211 602201507 2322512 19494273755/(3^20*2*9) 1/ 91.577 1/ 91.577 22 122787268 189819117 339063052 1611140121 6030293 27404894631/(3^21*2^8) 1/ 97.714 1/ 97.730 < corrected Nov.26, 2002 23 135262992 188192369 317179778 4316653453 16900541 724456628891/(3^22*2^11) 1/ 88.713 1/ 88.716 24 127291021 186332722 296065646 11536599329 44079555 25 138158255 184329176 275718564 30870338727 122379267 26 130507401 182115409 256293497 27 140020350 179769211 237801291 28 132658003 177328847 220340292 29 140981121 174764911 203868206 30 133952001 172102458 188376072 31 141154038 169356848 173877813 Maximum of probability 1/85.0135 (=1.2*10^10/141154038) 32 134455566 166528436 160334430 33 140700083 163699383 147690680 34 134352462 160804297 135910491 35 139746487 157891794 125015117 36 133703574 154921172 114889877 37 138344539 151951303 105503739 38 132603896 148951817 96834433 39 136574741 145960483 88835369 40 131126632 142986118 81433010 41 134520669 139992205 74636635 42 129312032 137032401 68359558 43 132185904 134093830 62589419 44 127246624 131158430 57272956 45 129674867 128269150 52402440 46 124964844 125374223 47912019 47 127005231 122527221 43796844 48 122508325 119702347 40036936 49 124161072 116928087 36582594 50 119898396 114193439 33414265 51 121257452 111482065 30509413 52 117187396 108815378 27859175 53 118239755 106181073 25434933 54 114363826 103592603 23208069 55 115221698 101060364 21168783 56 111470649 98564633 19314149 57 112098785 96103244 17619943 58 108596274 93693870 16060927 59 109001525 91332959 14641807 60 105622944 89008299 13366781 61 105914297 86738291 12173650 62 102674956 84484147 11088945 63 102798766 82299784 10113796 64 99727043 80174657 9212371 65 99731456 78083878 8389680 66 96781187 76020674 7647105 67 96665092 74013712 6968733 68 93846150 72046157 6343558 69 93655753 70143068 5781800 70 90958817 68252262 5260507 71 90663914 66427433 4788487 72 88091417 64640395 4362877 73 87751438 62870442 3971950 74 85267316 61175783 3618910 75 84843709 59481915 3291417 76 82492887 57868798 2999246 77 82025735 56275732 2729650 78 79772360 54734589 2482110 79 79281275 53219928 2259461 80 77118094 51733984 2057059 81 76581195 50284294 1871090 82 74510789 48905787 1701084 83 73920781 47519984 1550778 84 71940069 46190040 1411862 85 71334850 44890645 1282779 86 69453807 43630086 1169422 87 68822752 42392033 1060788 88 67006941 41191055 966781 89 66376985 40019927 878827 90 64642746 38876023 797658 91 64008953 37764646 727577 92 62331246 36686104 662350 93 61713663 35628719 600990 94 60093863 34609920 546953 95 59439896 33606877 498203 96 57919879 32635834 453233 97 57271105 31694918 411706 98 55800968 30777388 375028 99 55157523 29893436 340812 100 53744676 29009691 308987 101 53113388 28172735 282205 102 51757483 27335529 255963 103 51124806 26548022 232482 104 49826653 25766784 212119 105 49196254 25018908 192524 106 47946578 24282332 175395 107 47330035 23574870 159092 108 46144276 22873427 145533 109 45539843 22191367 131596 110 44389618 21538209 120270 111 43806080 20903255 108656 112 42716743 20285936 98789 113 42127302 19678705 89794 114 41066466 19097308 81725 115 40488406 18522605 74342 116 39493839 17975023 67761 117 38915241 17436142 61642 118 37957447 16921084 56065 119 37409314 16412074 50967 120 36488560 15918637 46234 121 35950145 15442412 42247 122 35068999 14974679 38245 123 34546377 14538495 34681 124 33694608 14091183 31597 125 33173253 13667919 28950 126 32362784 13256777 26014 127 31864063 12857041 23860 128 31093631 12469536 21627 129 30603807 12093643 19620 130 29863950 11725228 17836 131 29376456 11369550 16437 132 28680843 11025303 14901 133 28223390 10691000 13415 134 27534261 10368235 12073 135 27086718 10052136 11031 136 26432803 9742234 10141 137 25997519 9450937 9357 138 25379422 9160413 8287 139 24950342 8879610 7624 140 24362597 8611547 6907 141 23948558 8342151 6386 142 23365195 8088706 5738 143 22987712 7845930 5288 144 22427780 7597945 4657 145 22051460 7370671 4335 146 21525592 7137768 3913 147 21151217 6927818 3543 148 20645278 6711639 3347 149 20298191 6503763 2905 150 19804892 6305058 2637 151 19466940 6106668 2331 152 18999511 5919409 2143 153 18660840 5737979 1940 154 18218690 5564487 1739 155 17901306 5391709 1651 156 17473872 5223949 1483 157 17160516 5064047 1407 158 16752129 4906929 1213 159 16455153 4756298 1129 160 16069402 4611257 1022 161 15778123 4464877 989 162 15406031 4325899 912 163 15128189 4191612 750 164 14767025 4061146 656 165 14501099 3936464 656 166 14151753 3814796 589 167 13900883 3691687 545 168 13564357 3575654 447 169 13317429 3467437 401 170 13002764 3360841 402 171 12764551 3251776 343 172 12462186 3152392 322 173 12234948 3053621 290 174 11942950 2958579 278 175 11721832 2866845 249 176 11450728 2777954 213 177 11234417 2689352 214 178 10972207 2608909 191 179 10756778 2526575 144 180 10508388 2445392 155 181 10308591 2368512 149 182 10062294 2296749 115 183 9872794 2223442 122 184 9641308 2152662 109 185 9464402 2087020 84 186 9239365 2020211 87 187 9063711 1954785 72 188 8847949 1896195 68 189 8687420 1834509 82 190 8478336 1775586 57 191 8312408 1722659 53 192 8122166 1666240 46 193 7962070 1615665 46 194 7773696 1565321 39 195 7623893 1514529 40 196 7445479 1464253 32 197 7300771 1421992 28 198 7129009 1375997 24 199 6989233 1333214 30 200 6827532 1289563 19 201 6692388 1248386 25 202 6542525 1211396 11 203 6412433 1172382 11 204 6259337 1135726 16 205 6138858 1098934 9 206 5989284 1063878 12 207 5876733 1030524 14 208 5734865 998864 8 209 5622424 967701 9 210 5486785 936998 6 211 5385578 905431 10 212 5260591 878782 8 213 5151060 850707 10 214 5032273 823619 8 215 4931017 796288 2 216 4817628 772030 5 217 4721827 746165 5 218 4615307 725777 4 219 4522842 698460 6 220 4413422 677319 5 221 4324424 656685 4 222 4223561 634554 1 223 4134244 614938 3 224 4041661 594990 3 225 3961738 578849 0 226 3868301 558257 1 227 3789097 539966 2 228 3704651 524099 1 229 3627562 507191 2 230 3539783 490533 0 231 3471182 473863 0 232 3389254 459909 2 233 3318990 443793 1 234 3244818 431505 3 235 3177109 417847 0 236 3106319 403704 2 237 3044163 390520 0 238 2970781 379295 3 239 2910981 366997 1 240 2842507 355571 0 241 2779703 343246 0 242 2720638 332102 0 243 2664144 321710 2 244 2600510 310767 0 245 2545402 300757 1 246 2486281 291779 0 247 2434502 283127 0 248 2378426 273882 0 249 2332084 264658 0 250 2275858 255775 0 251 2227043 247370 0 252 2178300 239261 0 253 2131319 232982 0 254 2082324 225066 0 255 2039550 216888 0 256 1990080 210330 1 257 1954591 204195 0 258 1905476 197028 0 259 1867638 191373 0 260 1823035 185169 0 261 1784197 178464 0 262 1742315 173079 0 263 1705398 167558 0 264 1666592 162732 0 265 1633468 157000 0 266 1597318 152383 0 267 1561059 146869 0 268 1524789 142882 0 269 1491415 137890 0 270 1459323 133730 0 271 1425922 129027 0 272 1394332 124877 0 273 1365496 120384 0 274 1332674 117493 0 275 1304276 113115 0 276 1274323 109833 0 277 1247046 106109 0 278 1221084 102333 0 279 1194675 99379 0 280 1165852 96147 0 281 1143098 93102 0 282 1115403 89900 0 283 1091559 87485 0 284 1065805 84321 0 285 1044443 81694 0 286 1019200 79102 0 287 997541 76689 0 288 974059 73772 0 289 954649 71638 0 290 932560 69092 0 291 910837 67063 0 292 890875 64622 0 293 871465 63044 0 294 850270 61183 0 295 834856 58640 0 296 814280 56699 0 297 796699 54954 0 298 779848 53169 0 299 760910 51651 0 300 743616 49755 0 301 726842 47939 0 302 711602 46845 0 303 697035 45433 0 304 680112 43876 0 305 666343 42033 0 306 650121 40716 0 307 635849 39590 0 308 622535 38221 0 309 607708 37378 0 310 593912 36594 0 311 580319 34604 0 312 566769 33674 0 313 555420 32340 0 314 543302 31656 0 315 530321 30348 0 316 518742 29153 0 317 506583 28455 0 318 497146 27691 0 319 483657 26545 0 320 473483 25837 0 321 463407 25127 0 322 454156 24174 0 323 443028 23438 0 324 433694 22523 0 325 424470 22140 0 326 413952 20953 0 327 405329 20538 0 328 395763 19740 0 329 387856 19163 0 330 376831 18617 0 331 369208 17927 0 332 360018 17230 0 333 352572 16947 0 334 345169 16331 0 335 338693 15727 0 336 331246 15334 0 337 322442 14620 0 338 315344 14242 0 339 308268 13867 0 340 300468 13431 0 341 295682 12846 0 342 288391 12232 0 343 281422 12233 0 344 275452 11512 0 345 269635 11208 0 346 261796 10929 0 347 257677 10572 0 348 250742 10332 0 349 245330 9907 0 350 240600 9402 0 351 234598 9284 0 352 229601 8890 0 353 224084 8738 0 354 219143 8446 0 355 214554 8077 0 356 209821 8002 0 357 205622 7659 0 358 198975 7284 0 359 195362 7103 0 360 190691 6717 0 361 187360 6736 0 362 181968 6530 0 363 178692 6212 0 364 175147 6060 0 365 170203 5870 0 366 166955 5752 0 367 163333 5480 0 368 159295 5384 0 369 155471 5194 0 370 151976 5019 0 371 148548 4688 0 372 145062 4551 0 373 142087 4465 0 374 138952 4220 0 375 135919 4078 0 376 133542 4178 0 377 129610 4013 0 378 126421 3748 0 379 124416 3615 0 380 120844 3606 0 381 119211 3391 0 382 116155 3293 0 383 113274 3220 0 384 110943 3097 0 385 108237 2989 0 386 105728 2921 0 387 103289 2788 0 388 101723 2698 0 389 98674 2654 0 390 96026 2515 0 391 94854 2477 0 392 91651 2395 0 393 90718 2249 0 394 88166 2259 0 395 85609 2199 0 396 84011 2066 0 397 82436 2003 0 398 80245 1959 0 399 78616 1908 0 400 76479 1801 0 401 75295 1795 0 402 73484 1740 0 403 71994 1648 0 404 70542 1641 0 405 68448 1523 0 406 66803 1500 0 407 65329 1502 0 408 63999 1404 0 409 62538 1344 0 410 60558 1362 0 411 59925 1309 0 412 58717 1234 0 413 57067 1162 0 414 56141 1133 0 415 54362 1064 0 416 53107 1186 0 417 51952 1055 0 418 50886 1035 0 419 49370 921 0 420 48562 975 0 421 47374 903 0 422 46208 847 0 423 45425 896 0 424 44649 814 0 425 43225 780 0 426 42266 786 0 427 41130 764 0 428 40212 637 0 429 39699 662 0 430 38516 667 0 431 37762 644 0 432 36520 635 0 433 35865 618 0 434 35477 586 0 435 34705 525 0 436 33442 526 0 437 33151 525 0 438 31731 521 0 439 31295 505 0 440 30676 497 0 441 29663 453 0 442 29371 453 0 443 28579 441 0 444 27685 460 0 445 27298 409 0 446 26535 366 0 447 26230 327 0 448 25635 371 0 449 24876 342 0 450 24498 369 0 451 23689 360 0 452 23128 372 0 453 22609 320 0 454 22269 307 0 455 21695 300 0 456 21210 294 0 457 20772 271 0 458 20453 275 0 459 19696 287 0 460 19431 272 0 461 18946 203 0 462 18392 202 0 463 18080 220 0 464 17550 226 0 465 17231 220 0 466 16757 202 0 467 16440 183 0 468 16061 207 0 469 15694 182 0 470 15441 186 0 471 14963 152 0 472 14746 183 0 473 14373 193 0 474 13993 180 0 475 13768 144 0 476 13269 145 0 477 13220 134 0 478 12687 125 0 479 12572 152 0 480 12065 106 0 481 11955 119 0 482 11777 115 0 483 11478 94 0 484 11257 89 0 485 10801 95 0 486 10638 103 0 487 10291 112 0 488 10305 70 0 489 9933 92 0 490 9787 95 0 491 9533 97 0 492 9461 89 0 493 8918 78 0 494 8825 77 0 495 8655 71 0 496 8366 69 0 497 8220 81 0 498 8124 84 0 499 7784 64 0 500 7739 87 0 501 7588 65 0 502 7363 62 0 503 7276 68 0 504 7117 51 0 505 6731 55 0 506 6500 48 0 507 6530 32 0 508 6281 37 0 509 6222 48 0 510 6085 46 0 511 6102 43 0 512 5805 59 0 513 5572 23 0 514 5551 48 0 515 5603 40 0 516 5393 37 0 517 5317 35 0 518 5084 30 0 519 5002 28 0 520 4848 40 0 521 4745 26 0 522 4700 24 0 523 4532 31 0 524 4407 25 0 525 4312 28 0 526 4232 26 0 527 4053 22 0 528 4026 24 0 529 3840 21 0 530 3804 26 0 531 3725 23 0 532 3657 18 0 533 3577 24 0 534 3517 16 0 535 3259 18 0 536 3273 17 0 537 3174 31 0 538 3260 18 0 539 3133 14 0 540 3165 14 0 541 3049 15 0 542 2908 12 0 543 2946 15 0 544 2772 17 0 545 2604 15 0 546 2741 13 0 547 2672 11 0 548 2609 14 0 549 2531 9 0 550 2374 16 0 551 2391 12 0 552 2273 15 0 553 2257 8 0 554 2169 12 0 555 2140 10 0 556 2082 9 0 557 2077 10 0 558 1984 7 0 559 1969 13 0 560 1923 7 0 561 1880 7 0 562 1874 6 0 563 1824 10 0 564 1693 4 0 565 1746 9 0 566 1692 5 0 567 1657 5 0 568 1656 11 0 569 1587 6 0 570 1584 1 0 571 1466 8 0 572 1479 8 0 573 1452 7 0 574 1330 5 0 575 1313 5 0 576 1332 6 0 577 1258 8 0 578 1234 5 0 579 1174 1 0 580 1222 6 0 581 1231 4 0 582 1196 4 0 583 1058 3 0 584 1099 4 0 585 1119 5 0 586 1018 2 0 587 1006 6 0 588 1020 2 0 589 975 7 0 590 954 1 0 591 887 2 0 592 885 0 0 593 895 2 0 594 870 2 0 595 841 2 0 596 797 1 0 597 808 2 0 598 828 4 0 599 817 3 0 600 704 3 0 601 809 2 0 602 697 2 0 603 690 3 0 604 672 3 0 605 679 2 0 606 659 1 0 607 598 0 0 608 618 0 0 609 593 0 0 610 593 3 0 611 608 1 0 612 565 1 0 613 576 1 0 614 559 4 0 615 573 2 0 616 515 3 0 617 506 3 0 618 488 1 0 619 490 1 0 620 452 3 0 621 464 0 0 622 436 0 0 623 449 1 0 624 429 0 0 625 393 2 0 626 417 0 0 627 374 2 0 628 394 0 0 629 409 0 0 630 369 1 0 631 391 2 0 632 378 1 0 633 374 0 0 634 323 0 0 635 330 0 0 636 311 0 0 637 322 0 0 638 307 1 0 639 296 0 0 640 284 0 0 641 283 0 0 642 286 0 0 643 267 0 0 644 297 0 0 645 259 0 0 646 269 0 0 647 247 0 0 648 256 0 0 649 257 0 0 650 237 1 0 651 229 0 0 652 213 0 0 653 220 0 0 654 232 1 0 655 203 0 0 656 208 0 0 657 200 1 0 658 206 1 0 659 188 0 0 660 199 1 0 661 189 0 0 662 192 1 0 663 151 1 0 664 177 0 0 665 184 0 0 666 177 1 0 667 139 0 0 668 165 0 0 669 152 1 0 670 132 0 0 671 132 0 0 672 122 0 0 673 152 0 0 674 102 0 0 675 144 0 0 676 106 0 0 677 138 0 0 678 124 1 0 679 116 0 0 680 113 0 0 681 118 0 0 682 104 0 0 683 97 0 0 684 99 1 0 685 122 0 0 686 108 0 0 687 116 0 0 688 96 0 0 689 97 0 0 690 90 0 0 691 90 0 0 692 98 0 0 693 79 0 0 694 106 0 0 695 84 0 0 696 101 0 0 697 78 0 0 698 78 1 0 699 80 0 0 700 62 0 0 701 66 0 0 702 60 1 0 703 58 0 0 704 61 0 0 705 70 0 0 706 48 0 0 707 65 0 0 708 63 0 0 709 76 0 0 710 61 0 0 711 58 0 0 712 64 0 0 713 41 0 0 714 53 0 0 715 57 0 0 716 44 0 0 717 51 0 0 718 53 0 0 719 43 0 0 720 55 0 0 721 41 0 0 722 44 0 0 723 46 0 0 724 47 0 0 725 40 0 0 726 41 0 0 727 37 0 0 728 35 0 0 729 39 0 0 730 27 0 0 731 36 0 0 732 43 0 0 733 39 0 0 734 43 0 0 735 29 0 0 736 47 0 0 737 24 0 0 738 34 0 0 739 23 0 0 740 30 0 0 741 34 0 0 742 25 0 0 743 22 0 0 744 18 0 0 745 22 0 0 746 24 0 0 747 19 0 0 748 23 1 0 749 24 0 0 750 31 0 0 751 13 0 0 752 27 0 0 753 21 0 0 754 24 0 0 755 22 0 0 756 17 0 0 757 20 0 0 758 19 0 0 759 19 0 0 760 13 0 0 761 13 0 0 762 16 0 0 763 12 0 0 764 20 0 0 765 22 0 0 766 21 0 0 767 10 0 0 768 14 0 0 769 11 0 0 770 12 0 0 771 19 0 0 772 12 0 0 773 14 0 0 774 18 0 0 775 17 0 0 776 22 0 0 777 14 0 0 778 10 0 0 779 15 0 0 780 8 0 0 781 7 0 0 782 14 0 0 783 9 0 0 784 7 0 0 785 7 0 0 786 10 0 0 787 8 0 0 788 4 0 0 789 7 0 0 790 7 0 0 791 11 0 0 792 6 0 0 793 8 0 0 794 11 0 0 795 10 0 0 796 8 0 0 797 7 0 0 798 7 0 0 799 4 0 0 800 3 0 0 801 7 0 0 802 8 0 0 803 6 0 0 804 5 0 0 805 10 0 0 806 7 0 0 807 2 0 0 808 6 0 0 809 6 1 0 810 8 0 0 811 4 0 0 812 3 0 0 813 5 0 0 814 9 0 0 815 4 0 0 816 7 0 0 817 3 0 0 818 5 0 0 819 4 0 0 820 3 0 0 821 1 0 0 822 3 0 0 823 3 0 0 824 3 0 0 825 2 0 0 826 6 0 0 827 2 0 0 828 2 0 0 829 3 0 0 830 1 0 0 831 7 0 0 832 5 0 0 833 2 0 0 834 2 0 0 835 7 0 0 836 3 0 0 837 3 0 0 838 1 0 0 839 2 0 0 840 3 0 0 841 1 0 0 842 1 0 0 843 1 0 0 844 1 0 0 846 2 0 0 848 4 0 0 849 3 0 0 850 4 0 0 851 4 0 0 852 1 0 0 854 2 0 0 855 2 0 0 856 3 0 0 857 1 0 0 858 1 0 0 859 3 0 0 861 1 0 0 862 2 0 0 863 5 0 0 865 1 0 0 867 1 0 0 868 1 0 0 870 1 0 0 871 1 0 0 872 1 0 0 873 2 0 0 874 2 0 0 875 1 0 0 877 2 0 0 878 3 0 0 879 1 0 0 880 2 0 0 881 2 0 0 883 3 0 0 885 1 0 0 886 2 0 0 887 1 0 0 888 1 0 0 890 1 0 0 891 1 0 0 892 2 0 0 894 1 0 0 895 1 0 0 898 1 0 0 899 1 0 0 900 1 0 0 905 2 0 0 909 1 0 0 911 1 0 0 912 1 0 0 916 2 0 0 917 1 0 0 921 1 0 0 922 1 0 0 931 1 0 0 933 1 0 0 935 1 0 0 940 1 0 0 947 1 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