A148250 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, 1, -1), (1, -1, 1), (1, 0, 0)}.

1, 1, 2, 4, 13, 36, 123, 412, 1504, 5600, 21399, 84082, 335325, 1365925, 5631945, 23526240, 99401707, 423998705, 1825605301, 7920044895, 34608734002, 152221362735, 673469046190, 2996014337863, 13393435660905, 60149049644269, 271270358104602, 1228214195018762, 5581224940035092

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + 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: A148247 A148248 A148249 * A148251 A144924 A148252

Adjacent sequences: A148247 A148248 A148249 * A148251 A148252 A148253

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved