A149090 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), (-1, 0, 1), (-1, 1, 1), (1, 1, 0)}.

1, 1, 4, 7, 34, 73, 349, 817, 4042, 10069, 49507, 127873, 636262, 1693573, 8402032, 22820875, 113817454, 314673517, 1566987739, 4389038017, 21914474266, 62104354621, 309818244166, 886054108339, 4426647223768, 12765629703193, 63743452057729, 185072828494417, 924906132097252, 2702137210824097

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, -1 + j, -1 + k, -1 + n] + aux[1 + 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: A153062 A237424 A143547 * A103059 A123809 A140981

Adjacent sequences: A149087 A149088 A149089 * A149091 A149092 A149093

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved