A149206 - OEIS

A149206

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

1, 1, 4, 10, 40, 129, 540, 1897, 8246, 30665, 135859, 524585, 2358632, 9347568, 42477772, 171734447, 786713158, 3229974119, 14891910671, 61902473315, 286878483816, 1204680901628, 5606781805948, 23745404043392, 110910037745343, 473126392668984, 2216586236663657, 9514692779869440

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OFFSET

0,3

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A051479 A149204 A149205 * A149207 A156798 A149208

Adjacent sequences: A149203 A149204 A149205 * A149207 A149208 A149209

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved