A148822 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, 1, 0), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 8, 26, 94, 303, 1154, 4372, 15884, 62623, 244797, 953760, 3813186, 15279908, 61791682, 250255955, 1021461121, 4211124573, 17290514080, 71510272399, 298032145342, 1239217133213, 5174916533646, 21726875233801, 91258664336181, 384002548160385, 1621744022534430, 6863111651068515

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A148821 A074506 A215087 * A124528 A320344 A006870

Adjacent sequences: A148819 A148820 A148821 * A148823 A148824 A148825

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved