A151009 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, 0), (0, 1, 1), (1, -1, 0), (1, 0, -1), (1, 1, 1)}.

1, 2, 9, 39, 175, 816, 3873, 18546, 89585, 435652, 2128065, 10432329, 51295715, 252813922, 1248362621, 6174100841, 30576404553, 151594186090, 752300064451, 3736407707659, 18570435527151, 92353606575420, 459532372068109, 2287600603432482, 11392571991635033, 56757109998184240, 282851182557244863

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, -1 + k, -1 + 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, 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: A037632 A095939 A361358 * A151010 A151011 A151012

Adjacent sequences: A151006 A151007 A151008 * A151010 A151011 A151012

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved