A148059 - OEIS

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A148059

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

1, 1, 2, 3, 10, 22, 71, 174, 653, 1814, 6915, 20546, 82095, 257809, 1056914, 3465493, 14500386, 49162222, 209454739, 730286285, 3154572233, 11256937646, 49204919325, 179067026571, 790635748409, 2926364462640, 13031956988866, 48947868670643, 219613554134575, 835550047444947, 3773438077994772

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..30.

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[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, 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: A148056 A148057 A148058 * A089880 A271740 A130002

Adjacent sequences: A148056 A148057 A148058 * A148060 A148061 A148062

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved