A150326 - OEIS

A150326

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

1, 2, 7, 22, 87, 320, 1336, 5315, 22893, 95282, 418633, 1793723, 7989642, 34925906, 157138088, 696964277, 3159969123, 14169903709, 64636890808, 292319981145, 1340038059198, 6101495367060, 28084990750092, 128582966165169, 593913751706076, 2731546244668348, 12654204718537222, 58422240391365539

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OFFSET

0,2

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150324 A150325 A102311 * A150327 A150328 A150329

Adjacent sequences: A150323 A150324 A150325 * A150327 A150328 A150329

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved