A148137 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, 0), (-1, 0, -1), (0, -1, 1), (0, 1, 0), (1, 1, -1)}.

1, 1, 2, 4, 11, 28, 89, 266, 894, 2887, 10129, 34934, 126616, 454347, 1684358, 6242626, 23641108, 89693829, 345105492, 1333739582, 5208633463, 20435993351, 80769046108, 320745663196, 1281477639621, 5142830155160, 20736929789522, 83949701741692, 341269279316502, 1392422909701118, 5701204016762123

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A363454 A034768 A148136 * A148138 A005503 A148139

Adjacent sequences: A148134 A148135 A148136 * A148138 A148139 A148140

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved