A148731 - OEIS

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A148731

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

1, 1, 3, 7, 25, 74, 263, 839, 3093, 10516, 39141, 135910, 516046, 1838960, 7012773, 25280377, 97338047, 356457878, 1375147361, 5071061128, 19684481356, 73304618000, 284919096885, 1065890555506, 4160076321794, 15670885172070, 61209072473718, 231330383014222, 906253268260560, 3442378506411670

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A148729 A143339 A148730 * A148732 A151269 A130463

Adjacent sequences: A148728 A148729 A148730 * A148732 A148733 A148734

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved