A148232 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), (-1, 1, 0), (0, 0, -1), (1, -1, 1), (1, 0, 0)}.

1, 1, 2, 4, 13, 34, 111, 352, 1221, 4184, 15083, 55391, 205712, 779703, 2997654, 11661511, 45778491, 181783227, 728691627, 2937711675, 11944846339, 48899728232, 201293267995, 833025368003, 3467043404167, 14498558571508, 60864665286887, 256663357107545, 1086672027553058, 4615962185504438

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + 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: A148230 A227808 A148231 * A148233 A148234 A284335

Adjacent sequences: A148229 A148230 A148231 * A148233 A148234 A148235

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved