A149118 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, 0), (-1, 0, 0), (0, -1, 1), (1, 1, 0)}.

1, 1, 4, 9, 32, 103, 345, 1275, 4410, 16741, 61731, 233495, 902378, 3437487, 13553036, 52676569, 208717276, 828362597, 3294044819, 13255061489, 53113955276, 215179562527, 870783523200, 3541185265429, 14454981038936, 59025273287545, 242367745510571, 994814873513383, 4100366928340036

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, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A149115 A149116 A149117 * A149119 A149120 A219151

Adjacent sequences: A149115 A149116 A149117 * A149119 A149120 A149121

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved