A149619 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), (1, -1, -1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 65, 241, 1075, 4449, 20177, 87403, 402719, 1796813, 8377087, 38115979, 179267151, 827203021, 3917268679, 18268401439, 86985225021, 409018283113, 1956232886103, 9259302756775, 44448987332093, 211521435478525, 1018574704606631, 4868813224782789, 23508260477228249, 112793042604351915

Offset

0,3

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

Crossrefs

Sequence in context: A149617 A149618 A323793 * A149620 A149621 A149622

Adjacent sequences: A149616 A149617 A149618 * A149620 A149621 A149622

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved