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.

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

1,1

Links

Table of n, a(n) for n=1..45.

Scott R. Shannon, Data for n=1 to n=14.

Formula

For w>=n, T(n,w) = A116904(n).

Example

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;

Crossrefs

Cf. A337400 (start at middle of tube), A337403 (start at tube's edge), A116904 (w->infinity), A001412, A337023, A259808, A039648.

Sequence in context: A260645 A226658 A212153 * A338127 A243018 A032731

Adjacent sequences: A337398 A337399 A337400 * A337402 A337403 A337404

Keyword

nonn,walk,tabl

Author

Scott R. Shannon, Aug 26 2020

Status

approved