A148392 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, 0), (0, 1, 0), (1, -1, 1), (1, 0, -1)}.

1, 1, 2, 5, 16, 52, 178, 625, 2229, 8292, 31844, 123850, 487577, 1939259, 7783926, 31652369, 130184871, 539206880, 2246282327, 9408346891, 39623252299, 167927239399, 715732297981, 3063454084931, 13158541339027, 56712257652225, 245295621094005, 1064945938445083, 4639147279079300

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A232317 A148391 A337268 * A149956 A149957 A148393

Adjacent sequences: A148389 A148390 A148391 * A148393 A148394 A148395

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved