A148164 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, 0, 1), (-1, 1, 0), (0, -1, 1), (0, 1, 0), (1, 0, -1)}.

1, 1, 2, 4, 11, 31, 98, 314, 1079, 3773, 13757, 50953, 193733, 747508, 2936032, 11676165, 47046523, 191533397, 787652467, 3267141729, 13661333890, 57536418899, 243931400240, 1040437757637, 4462518009660, 19238441448717, 83332985149012, 362554049022875, 1583800968801745, 6945130288469293

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A119020 A073191 A173139 * A364594 A213091 A148165

Adjacent sequences: A148161 A148162 A148163 * A148165 A148166 A148167

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved