A148130 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), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 11, 27, 82, 228, 741, 2204, 7439, 23265, 80801, 261285, 925254, 3073545, 11054792, 37460250, 136318642, 469722070, 1726066940, 6026557952, 22317897676, 78816482647, 293824628003, 1047421676406, 3926284015297, 14112557498365, 53156509703810, 192406657606086, 727695258089618, 2650547548516870

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, j, 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: A086441 A316696 A319616 * A350030 A131482 A234845

Adjacent sequences: A148127 A148128 A148129 * A148131 A148132 A148133

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved