A148228 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, 0, 1), (-1, 1, -1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 13, 32, 112, 317, 1199, 3650, 14390, 46288, 187934, 628364, 2608187, 8985156, 37900208, 133703155, 571404787, 2054685733, 8871770591, 32416109883, 141169696693, 522777139834, 2292885433332, 8589464293407, 37900674076646, 143404002717644, 636046108002097, 2427716350295630

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A000866 A320424 A148227 * A148229 A148230 A227808

Adjacent sequences: A148225 A148226 A148227 * A148229 A148230 A148231

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved