A149911 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), (0, 1, 0), (1, -1, -1), (1, 0, 0)}.

1, 2, 5, 15, 45, 148, 507, 1804, 6639, 25021, 96028, 375278, 1486861, 5967550, 24225135, 99306572, 410630017, 1711438826, 7182427194, 30337840617, 128889250395, 550511528467, 2362816922082, 10187233185111, 44103750496501, 191680538110624, 836046583061122, 3658812381578840, 16062094437778204

Offset

0,2

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, 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: A149908 A149909 A149910 * A148357 A149912 A148358

Adjacent sequences: A149908 A149909 A149910 * A149912 A149913 A149914

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved