A149061 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, 0, 1), (-1, 1, 0), (0, 1, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 3, 11, 39, 155, 629, 2635, 11375, 49775, 221993, 1000469, 4559119, 20954301, 97007355, 452068093, 2117955301, 9972403285, 47151732371, 223801633257, 1065825239793, 5091269173915, 24386527347883, 117095676603227, 563513272181635, 2717367767033319, 13128069939371165, 63531808704306035

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A281482 A132889 A245390 * A149062 A066979 A333548

Adjacent sequences: A149058 A149059 A149060 * A149062 A149063 A149064

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved