

A337401


Triangle read by rows: T(n,w) is the number of nstep 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.


3



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
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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 2step 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



