A149858 - OEIS

A149858

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

1, 2, 5, 13, 38, 119, 388, 1297, 4434, 15473, 54774, 196163, 709908, 2592189, 9535661, 35301132, 131431439, 491791103, 1848203446, 6972841221, 26399271376, 100262275132, 381866112379, 1458144417559, 5580938194398, 21406277740406, 82266779029469, 316730158315437, 1221446501570766, 4717637748636774

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OFFSET

0,2

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[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: A360271 A343937 A369729 * A148303 A148304 A149859

Adjacent sequences: A149855 A149856 A149857 * A149859 A149860 A149861

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved