A149723 - OEIS

A149723

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

1, 1, 5, 17, 75, 285, 1309, 5515, 25679, 112633, 530845, 2393671, 11381751, 52290385, 250260427, 1165119535, 5604533791, 26355813965, 127289400889, 603273589021, 2923117726291, 13939944270725, 67727672763965, 324616185194801, 1580747352700737, 7608095484588771, 37120200203145903, 179283568333680023

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OFFSET

0,3

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 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: A166228 A362177 A102387 * A149724 A149725 A149726

Adjacent sequences: A149720 A149721 A149722 * A149724 A149725 A149726

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved