A150708 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, 1, 1), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 26, 122, 452, 2208, 8698, 42938, 175234, 870066, 3635546, 18103834, 76938626, 383743186, 1651914246, 8246876034, 35861486132, 179131833684, 785374015858, 3924378294226, 17323510220366, 86581425739210, 384410552266316, 1921519678244308, 8573682536880550, 42860427587164794, 192066028460933972

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, -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] + 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: A150705 A150706 A150707 * A150709 A130613 A143338

Adjacent sequences: A150705 A150706 A150707 * A150709 A150710 A150711

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved