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A148453 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, 0), (-1, 0, 0), (0, 0, 1), (1, -1, 0), (1, 1, -1)} 0
1, 1, 2, 6, 17, 53, 181, 629, 2273, 8442, 31903, 123276, 482016, 1909749, 7671004, 31041259, 126847637, 522862741, 2167729171, 9053158292, 38026043662, 160503188086, 681190257778, 2902953020464, 12422813296300, 53381627069382, 230129554758325, 995583076288227, 4320678366122981 (list; graph; refs; listen; history; text; internal format)
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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A148451 A148452 A307975 * A097514 A108630 A161408

Adjacent sequences:  A148450 A148451 A148452 * A148454 A148455 A148456

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 15 14:06 EST 2019. Contains 329149 sequences. (Running on oeis4.)