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A148457 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, 0, 1), (-1, 1, 1), (0, 0, 1), (1, 1, -1)} 0
1, 1, 2, 6, 18, 55, 191, 641, 2338, 8412, 31626, 118683, 457359, 1763742, 6931137, 27261381, 108770025, 434387917, 1753998833, 7090521404, 28908852160, 118022306253, 485066186991, 1996484012579, 8261227549240, 34234587581788, 142482320374052, 593868063996294, 2484063713185947 (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[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A006725 A066158 A148456 * A182881 A002999 A091142

Adjacent sequences:  A148454 A148455 A148456 * A148458 A148459 A148460

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified August 27 19:53 EDT 2015. Contains 261098 sequences.