A148779 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, 1), (-1, 0, 0), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 8, 23, 81, 264, 916, 3390, 12224, 46138, 175706, 669624, 2618701, 10257321, 40497341, 161706408, 646521499, 2607025411, 10570576931, 42983272026, 175815936337, 721178635794, 2968368865163, 12267812623937, 50818458789676, 211155535437719, 879646998027778, 3672049320661053

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A307875 A321730 A047143 * A148780 A148781 A327151

Adjacent sequences: A148776 A148777 A148778 * A148780 A148781 A148782

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved