A148423 - OEIS

A148423

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

1, 1, 2, 5, 18, 59, 210, 771, 2996, 11644, 46638, 190413, 785883, 3269350, 13802880, 58805780, 251800165, 1085863136, 4718853763, 20599960049, 90292141257, 397829888521, 1760283533023, 7811722003196, 34783756873350, 155429698073397, 696354098036891, 3127128078447276, 14080315363387703

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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, -1 + j, k, -1 + n] + aux[i, -1 + 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: A148420 A148421 A148422 * A148424 A148425 A286317

Adjacent sequences: A148420 A148421 A148422 * A148424 A148425 A148426

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved