A337401
Triangle read by rows: T(n,w) is the number of n-step self avoiding walks on a 3D cubic lattice confined inside a tube of cross section 2w X 2w where the walk starts at the center of the tube's side.
Original entry on oeis.org
5, 19, 21, 72, 91, 93, 258, 383, 407, 409, 926, 1638, 1821, 1851, 1853, 3176, 6856, 8019, 8295, 8331, 8333, 11000, 28810, 35506, 37531, 37921, 37963, 37965, 36988, 119106, 155492, 168399, 171691, 172215, 172263, 172265, 125302, 492766, 683126, 758182, 781811, 786823, 787501, 787555, 787557
Offset: 1
T(2,1) = 19 as after a step in one of the two directions toward the adjacent tube side the walk must turn along the side; this eliminates the 2-step straight walk in those two directions, so the total number of walks is 4*4 + 5 - 2 = 19.
The table begins:
5;
19,21;
72,91,93;
258,383,407,409;
926,1638,1821,1851,1853;
3176,6856,8019,8295,8331,8333;
11000,28810,35506,37531,37921,37963,37965;
36988,119106,155492,168399,171691,172215,172263,172265;
125302,492766,683126,758182,781811, 786823,787501,787555,787557;
414518,2013142,2981996,3393526,3545117,3585297,3592551,3593403,3593463,3593465;
A338125
Triangle read by rows: T(n,w) is the number of n-step self avoiding walks on a 3D cubic lattice confined between two infinite planes a distance 2w apart where the walk starts at the middle point between the planes.
Original entry on oeis.org
6, 28, 30, 124, 148, 150, 516, 692, 724, 726, 2156, 3196, 3492, 3532, 3534, 8804, 14324, 16428, 16876, 16924, 16926, 36388, 64076, 76956, 80700, 81332, 81388, 81390, 148452, 282716, 354740, 380964, 387052, 387900, 387964, 387966, 609812, 1251044, 1631420, 1795212, 1843452, 1852716, 1853812, 1853884, 1853886
Offset: 1
T(2,1) = 28 as after a step in one of the two directions towards the planes the walk must turn along the plane; this eliminates the 2-step straight walk in those two directions, so the total number of walks is A001412(2) - 2 = 30 - 2 = 28.
The table begins:
6;
28,30;
124,148,150;
516,692,724,726;
2156,3196,3492,3532,3534;
8804,14324,16428,16876,16924,16926;
36388,64076,76956,80700,81332,81388,81390;
148452,282716,354740,380964,387052,387900,387964,387966;
609812,1251044,1631420,1795212,1843452,1852716,1853812,1853884,1853886;
2478484,5493804,7431100,8377908,8712892,8795020,8808420,8809796,8809876,8809878;
A337403
Table read by antidiagonals: T(w,n) is the number of n-step self avoiding walks on a 3D cubic lattice confined inside a tube of cross section w x w where the walk starts at the tube's edge.
Original entry on oeis.org
4, 12, 4, 36, 14, 4, 98, 54, 14, 4, 274, 200, 56, 14, 4, 702, 744, 224, 56, 14, 4, 1854, 2626, 926, 226, 56, 14, 4, 4614, 9186, 3738, 956, 226, 56, 14, 4, 11778, 31122, 15056, 4014, 958, 226, 56, 14, 4, 28914, 105766, 59092, 17074, 4050, 958, 226, 56, 14, 4
Offset: 1
T(1,2) = 12 as after a step in one of the two directions toward the adjacent tube edge the walk must turn along the side; this eliminates the 2-step straight walk in those two directions, so the total number of walks is 2*3 + 2*4 - 2 = 12.
The table begins:
4 12 36 98 274 702 1854 4614 11778 28914 72394 176310 435346...
4 14 54 200 744 2626 9186 31122 105766 351798 1175726 3859350 12729142...
4 14 56 224 926 3738 15056 59092 230254 881850 3367124 12712194 47952018...
4 14 56 226 956 4014 17074 71774 301578 1251362 5170636 21143094 86148002...
4 14 56 226 958 4050 17464 75060 325064 1400650 6040372 25882446 110668184...
4 14 56 226 958 4052 17506 75584 330070 1440668 6321926 27685144 121407404...
4 14 56 226 958 4052 17508 75632 330748 1447916 6386092 28180426 124857572...
4 14 56 226 958 4052 17508 75634 330802 1448768 6396174 28278426 125681952...
4 14 56 226 958 4052 17508 75634 330804 1448828 6397220 28292004 125825794...
4 14 56 226 958 4052 17508 75634 330804 1448830 6397286 28293264 125843600...
4 14 56 226 958 4052 17508 75634 330804 1448830 6397288 28293336 125845094...
4 14 56 226 958 4052 17508 75634 330804 1448830 6397288 28293338 125845172...
4 14 56 226 958 4052 17508 75634 330804 1448830 6397288 28293338 125845174...
A338126
Triangle read by rows: T(n,w) is the number of n-step self avoiding walks on a 3D cubic lattice confined between two infinite planes a distance w apart where the walk starts on one of the planes.
Original entry on oeis.org
5, 20, 21, 80, 92, 93, 304, 392, 408, 409, 1168, 1684, 1832, 1852, 1853, 4348, 7036, 8084, 8308, 8332, 8333, 16336, 29396, 35752, 37620, 37936, 37964, 37965, 60208, 120776, 155756, 168768, 171808, 172232, 172264, 172265, 223352, 497196, 677856, 758340, 782344, 786972, 787520, 787556, 787557
Offset: 1
T(2,1) = 20 as after one step towards the opposite plane the walk must turn along that plane; this eliminates the 2-step straight walk in that direction, so the total number of walks is A116904(2) - 1 = 21 - 1 = 20.
The table begins:
5;
20,21;
80,92,93;
304,392,408,409;
1168,1684,1832,1852,1853;
4348,7036,8084,8308,8332,8333;
16336,29396,35752,37620,37936,37964,37965;
60208,120776,155756,168768,171808,172232,172264,172265;
223352,497196,677856,758340,782344,786972,787520,787556,787557;
817852,2026220,2920764,3379476,3545108,3586040,3592736,3593424,3593464,3593465;
A338127
Triangle read by rows: T(n,w) is the number of n-step self avoiding walks on a 3D cubic lattice confined between two infinite horizontal planes a distance 2w apart and an orthogonal plane on the y-z axes, where the walk starts at the middle point between the planes on the y-z plane.
Original entry on oeis.org
5, 19, 21, 73, 91, 93, 275, 383, 407, 409, 1075, 1639, 1821, 1851, 1853, 4133, 6881, 8019, 8295, 8331, 8333, 16249, 29155, 35507, 37531, 37921, 37963, 37965, 63293, 122491, 155525, 168399, 171691, 172215, 172263, 172265, 249445, 519351, 683711, 758183, 781811, 786823, 787501, 787555, 787557
Offset: 1
T(2,1) = 19 as after a step in one of the two directions towards the horizontal planes the walk must turn along the planes; this eliminates the 2-step straight walks in those two directions, so the total number of walks is A116904(2) - 2 = 21 - 2 = 19.
The table begins:
5;
19, 21;
73, 91, 93;
275, 383, 407, 409;
1075, 1639, 1821, 1851, 1853;
4133, 6881, 8019, 8295, 8331, 8333;
16249, 29155, 35507, 37531, 37921, 37963, 37965;
63293, 122491, 155525, 168399, 171691, 172215, 172263, 172265;
249445, 519351, 683711, 758183, 781811, 786823, 787501, 787555, 787557;
Showing 1-5 of 5 results.