A148650 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, 1, -1), (0, 0, 1), (1, 0, -1), (1, 1, -1)}.

1, 1, 3, 6, 24, 60, 247, 725, 3142, 9976, 44566, 150364, 683268, 2409852, 11098347, 40453800, 188206351, 704307402, 3302109484, 12625419479, 59563688027, 231816392010, 1099281724137, 4342743536033, 20681409598268, 82754124982121, 395518720240174, 1600228685069442, 7671788362735186

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, 1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A047167 A271428 A148649 * A148651 A148652 A148653

Adjacent sequences: A148647 A148648 A148649 * A148651 A148652 A148653

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved