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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)} 0
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 (list; graph; refs; listen; history; text; internal format)
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: A037737 A037632 A095939 * A151010 A151011 A151012

Adjacent sequences:  A151006 A151007 A151008 * A151010 A151011 A151012

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 25 00:48 EDT 2020. Contains 337333 sequences. (Running on oeis4.)