A150436 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), (0, 1, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 24, 99, 407, 1776, 7835, 35400, 161472, 746382, 3474604, 16300338, 76908464, 364715409, 1736718508, 8301812970, 39807939808, 191423730408, 922824490028, 4458571378237, 21583898594952, 104676864185763, 508468611377079, 2473498648120590, 12048802278297781, 58762633391661819, 286908179389872434

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[-1 + i, j, k, -1 + n] + aux[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: A162044 A150434 A150435 * A197553 A213950 A123764

Adjacent sequences: A150433 A150434 A150435 * A150437 A150438 A150439

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved