A148419 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, 0, 1), (0, 0, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 5, 18, 55, 207, 743, 2985, 11353, 47403, 189357, 806155, 3320235, 14415972, 60735227, 266952886, 1145375129, 5086266398, 22115900587, 99046871930, 435563614895, 1963427989281, 8712809726805, 39504708871655, 176630113016701, 804666823915117, 3621130775827235, 16564743136423270

Offset

0,3

Links

Table of n, a(n) for n=0..28.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A275079 A148417 A148418 * A148420 A148421 A148422

Adjacent sequences: A148416 A148417 A148418 * A148420 A148421 A148422

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved