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A150226 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), (0, 1, -1), (0, 1, 1), (1, 0, 1)} 0
1, 2, 6, 21, 86, 318, 1349, 5654, 23674, 102512, 451457, 1952965, 8704458, 38982187, 172994207, 781645957, 3548152605, 15981222319, 72960968130, 334143804197, 1521158967813, 6995945513819, 32254048901878, 147980022782907, 684415068561784, 3171558963632792, 14638033549230360, 68001159203716587 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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[i, -1 + 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, 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: A099947 A121726 A090805 * A326335 A256180 A150227

Adjacent sequences:  A150223 A150224 A150225 * A150227 A150228 A150229

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified July 15 14:28 EDT 2019. Contains 325031 sequences. (Running on oeis4.)