A150482 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, 0), (0, -1, 1), (0, 1, 1), (1, 1, 0)}.

1, 2, 7, 25, 100, 399, 1684, 7090, 30698, 133650, 588793, 2611114, 11660162, 52328699, 236097821, 1069202574, 4860527354, 22164421184, 101359319576, 464728029665, 2135700663533, 9835260769329, 45380407804743, 209750612440546, 971049114127696, 4502217093461595, 20902965657403973, 97172741760532582

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, -1 + j, k, -1 + n] + aux[i, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A150479 A150480 A150481 * A150483 A150484 A150485

Adjacent sequences: A150479 A150480 A150481 * A150483 A150484 A150485

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved