A151135 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, 0), (0, 1, 0), (1, 0, 1), (1, 1, -1), (1, 1, 0)}

1, 3, 11, 46, 199, 892, 4076, 18863, 88311, 416493, 1977383, 9436019, 45216124, 217454726, 1048858778, 5072181339, 24582872384, 119374899206, 580683017523, 2828923111284, 13800469252031, 67405302673001, 329588546389765, 1613183039259949, 7902963915750427, 38748812549009285, 190133662073199299

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, 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: A365449 A027135 A151134 * A307816 A151136 A151137

Adjacent sequences: A151132 A151133 A151134 * A151136 A151137 A151138

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved