A150458 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, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 25, 96, 396, 1663, 7216, 31878, 142690, 647948, 2965959, 13697703, 63689016, 297749767, 1399436219, 6604167136, 31286749357, 148712785585, 708904645509, 3388403109065, 16233340984760, 77938099379067, 374912838489914, 1806618128532500, 8719731573839590, 42147772529895546, 204001739070927948

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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[-1 + i, j, k, -1 + n] + aux[i, -1 + 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: A150457 A355628 A276903 * A150459 A150460 A150461

Adjacent sequences: A150455 A150456 A150457 * A150459 A150460 A150461

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved