A150520 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), (0, 1, 0), (1, -1, -1), (1, 1, 1)}.

1, 2, 7, 25, 103, 434, 1887, 8340, 37419, 169974, 779649, 3606069, 16784025, 78569084, 369536333, 1745293573, 8272862239, 39339883900, 187602333559, 896904874283, 4297782452363, 20636379410272, 99273842193385, 478382331583024, 2308825962338795, 11159098836879740, 54005730278815949, 261685526720366849

Offset

0,2

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, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, 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: A150517 A150518 A150519 * A150521 A150522 A150523

Adjacent sequences: A150517 A150518 A150519 * A150521 A150522 A150523

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved