A151100 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, 0), (-1, 1, -1), (1, 0, 0), (1, 0, 1), (1, 1, 0)}.

1, 3, 11, 43, 182, 783, 3498, 15732, 72351, 333779, 1562617, 7327464, 34715725, 164627999, 786629414, 3760854191, 18084444360, 86994234392, 420369148831, 2031847737290, 9856242149346, 47821651708499, 232704026736014, 1132557455930221, 5525341192048507, 26960333594715805, 131813633127893235

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A049169 A049175 A049158 * A063031 A151101 A151102

Adjacent sequences: A151097 A151098 A151099 * A151101 A151102 A151103

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved