A148454 - OEIS

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A148454

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

1, 1, 2, 6, 17, 57, 205, 745, 2875, 11305, 45332, 186380, 774303, 3267037, 13949978, 60078464, 261420213, 1145680231, 5056693164, 22468775276, 100367233789, 450802933329, 2034271914025, 9219038987323, 41952247315081, 191591933975581, 878015079137772, 4036487462078620, 18610889183478567

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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, -1 + 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: A190915 A032132 A339223 * A363042 A007743 A000687

Adjacent sequences: A148451 A148452 A148453 * A148455 A148456 A148457

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved