login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

A149608
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, 1), (-1, 1, 0), (1, 0, -1), (1, 1, 1)}
0
1, 1, 5, 15, 63, 217, 999, 3757, 17793, 69809, 334365, 1361721, 6570421, 27323139, 132784185, 561952215, 2743176341, 11766979961, 57626807759, 249837943569, 1226981605029, 5366122994625, 26411834991123, 116363366768863, 573725892578869, 2543389304313541, 12558714178737849, 55970650933680377
OFFSET
0,3
LINKS
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, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A019045 A191678 A149607 * A149609 A149610 A149611
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved