A148127 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, 1, -1), (0, 1, 0), (1, -1, 0)}.

1, 1, 2, 4, 11, 26, 75, 221, 666, 2059, 6659, 21851, 72248, 246377, 845284, 2944154, 10364180, 36881317, 132306401, 478964897, 1747856485, 6414446498, 23719301449, 88172846733, 329710429245, 1238865097474, 4677421758687, 17738834974568, 67552866289627, 258292786891009, 991012738396710, 3816085708899744

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + 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: A148124 A148125 A148126 * A148128 A148129 A340651

Adjacent sequences: A148124 A148125 A148126 * A148128 A148129 A148130

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved