A149353 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, 0, 0), (-1, 1, 1), (0, -1, 0), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 12, 42, 158, 614, 2432, 9999, 41656, 176122, 756265, 3282145, 14366101, 63486090, 282547790, 1265206244, 5701051412, 25822151736, 117485179665, 536948393330, 2463588074555, 11342489661409, 52399400212633, 242805491468364, 1128190614409404, 5256119344420086, 24547088662581941

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149350 A149351 A149352 * A149354 A197659 A360468

Adjacent sequences: A149350 A149351 A149352 * A149354 A149355 A149356

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved