A148702 - OEIS

A148702

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

1, 1, 3, 7, 23, 71, 241, 827, 2969, 10719, 39869, 149412, 568421, 2188494, 8488370, 33235585, 131138445, 520203906, 2078395161, 8342877038, 33647604003, 136384448249, 554714145737, 2265211261374, 9282805581252, 38149282176628, 157293038322763, 650217712657603, 2694590903013221

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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[i, j, 1 + 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: A106936 A088704 A341072 * A194691 A148703 A302180

Adjacent sequences: A148699 A148700 A148701 * A148703 A148704 A148705

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved