A149499 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, -1, -1), (1, 1, 1)}.

1, 1, 5, 9, 45, 109, 545, 1553, 7765, 24117, 120585, 396969, 1984845, 6813153, 34065765, 120666321, 603331605, 2190578173, 10952890865, 40569468449, 202847342245, 763846716897, 3819233584485, 14583041787425, 72915208937125, 281740598296225, 1408702991481125, 5499437584957425, 27497187924787125

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 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: A149496 A149497 A149498 * A100305 A149500 A149501

Adjacent sequences: A149496 A149497 A149498 * A149500 A149501 A149502

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved