A148995 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, 0), (0, 1, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 3, 9, 33, 117, 453, 1775, 7112, 28983, 120132, 504174, 2146646, 9208343, 39778905, 173078627, 757217899, 3328960216, 14708426707, 65283892983, 291015312216, 1302008131740, 5842963924992, 26296807422445, 118666236830752, 536772492146077, 2433653602795155, 11058875016376168, 50361354298500484

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A148992 A148993 A148994 * A148996 A255713 A148997

Adjacent sequences: A148992 A148993 A148994 * A148996 A148997 A148998

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved