A148662 - OEIS

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A148662

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

1, 1, 3, 6, 25, 69, 297, 919, 4209, 14330, 66413, 237589, 1127925, 4224288, 20166864, 77647110, 375206178, 1483748803, 7192465521, 28949796874, 141317035936, 578798473432, 2831000009495, 11738326687294, 57666232555593, 242042851859253, 1190667232643237, 5042932509993216, 24879899873021542

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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, j, 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] + 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: A148659 A148660 A148661 * A148663 A361288 A266549

Adjacent sequences: A148659 A148660 A148661 * A148663 A148664 A148665

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved