A148456 - OEIS

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A148456

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

1, 1, 2, 6, 18, 55, 187, 665, 2404, 8914, 33984, 131733, 517871, 2062976, 8320703, 33890091, 139284855, 577018589, 2408280217, 10116043988, 42749394792, 181625736257, 775565368155, 3326762767141, 14331173453690, 61976013148146, 269005365757008, 1171533077777764, 5118392288259919

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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[i, j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A000778 A006725 A066158 * A148457 A182881 A291730

Adjacent sequences: A148453 A148454 A148455 * A148457 A148458 A148459

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved