A151099 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, 0, 1), (0, 0, 1), (1, 0, 0), (1, 1, 0)}.

1, 3, 11, 43, 181, 787, 3491, 15766, 72213, 333972, 1556483, 7305176, 34479175, 163466387, 778101574, 3716946760, 17808521929, 85545387623, 411903327431, 1987499971566, 9607721942704, 46522582503969, 225619346235805, 1095696997537555, 5327841891158836, 25936928909187264, 126401369551320654

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A151098 A277220 A338999 * A049184 A049169 A049175

Adjacent sequences: A151096 A151097 A151098 * A151100 A151101 A151102

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved