A148512 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, 0), (0, 1, -1), (1, 0, 0)}.

1, 1, 3, 5, 17, 36, 128, 327, 1170, 3455, 12262, 40081, 142049, 495130, 1772625, 6418214, 23385253, 86616111, 321736427, 1210203620, 4573329384, 17419545738, 66751989887, 257123568873, 996294459849, 3876599461115, 15158851798617, 59508213689256, 234538307571314, 927776682371497, 3682212368039974

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A215396 A130844 A148511 * A148513 A148514 A105894

Adjacent sequences: A148509 A148510 A148511 * A148513 A148514 A148515

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved