A148501 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, -1, 0), (0, 0, 1), (0, 1, -1), (1, 0, -1)}.

1, 1, 3, 5, 15, 33, 111, 299, 1005, 2899, 9631, 30333, 103763, 345293, 1180645, 3990591, 13855337, 48420601, 171794343, 608614059, 2163454701, 7734113089, 27936343669, 101650409209, 371092684689, 1354799724367, 4961611103091, 18279863461215, 67772742040869, 252117779098577, 938394519450469, 3496508702500505

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, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A262326 A148499 A148500 * A148502 A295614 A089485

Adjacent sequences: A148498 A148499 A148500 * A148502 A148503 A148504

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved