A148782 - OEIS

A148782

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

1, 1, 3, 8, 24, 76, 249, 828, 2810, 9685, 33665, 117907, 416736, 1480881, 5284589, 18955873, 68263775, 246532461, 893166098, 3245162305, 11816472278, 43118632373, 157670651123, 577552892619, 2118935278521, 7786118829049, 28650470771100, 105556357505690, 389368526700961, 1437900059073162

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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, -1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A182453 A047087 A000958 * A148783 A084205 A118099

Adjacent sequences: A148779 A148780 A148781 * A148783 A148784 A148785

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved