A148265 - OEIS

A148265

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

1, 1, 2, 4, 14, 33, 121, 331, 1288, 3816, 15360, 48275, 199143, 651625, 2739341, 9243475, 39389281, 136285772, 586860958, 2073159057, 9003292399, 32364139558, 141560810053, 516376441034, 2272589047201, 8393750602328, 37136818932093, 138654180312227, 616235540380268, 2322801107486821

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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, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A148262 A148263 A148264 * A148266 A000622 A088028

Adjacent sequences: A148262 A148263 A148264 * A148266 A148267 A148268

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved