A149234 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, -1), (-1, 0, 0), (-1, 0, 1), (0, -1, 0), (1, 1, 0)}.

1, 1, 4, 11, 34, 123, 419, 1501, 5732, 20925, 80815, 314395, 1209220, 4820559, 19083662, 75911851, 307724890, 1237790403, 5033871995, 20612532057, 84134008596, 346989672093, 1432118446248, 5918323829069, 24628670168512, 102394999382253, 427288651678265, 1789242768786287, 7490596712558988

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, -1 + j, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A006765 A151272 A112272 * A149235 A149236 A135919

Adjacent sequences: A149231 A149232 A149233 * A149235 A149236 A149237

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved