A148069 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, -1, 1), (-1, 0, -1), (-1, 1, 1), (1, 0, 0)}.

1, 1, 2, 3, 12, 25, 97, 217, 872, 2073, 8739, 21791, 94168, 242515, 1052724, 2768883, 12208052, 32759425, 146062195, 398210911, 1784256044, 4923235527, 22189335102, 61880489173, 280668260110, 790141842345, 3597552961167, 10206542166177, 46623204529182, 133170203047901, 610549741362451, 1754713551161917

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, 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, -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: A148066 A148067 A148068 * A148070 A187994 A016021

Adjacent sequences: A148066 A148067 A148068 * A148070 A148071 A148072

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved