A337456
Number of n-step self-avoiding walks on a 3D cubic lattice where the walk consists of three different units and each unit cannot be adjacent to another unit of the same type.
Original entry on oeis.org
1, 6, 30, 126, 534, 2262, 9534, 40254, 169302, 702510, 2929806, 12222414, 50908158, 212134902, 882794118, 3654001326, 15159263934, 62906444238, 260853828438, 1081924309806, 4484440327350
Offset: 1
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;
Comments