A150134 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, 0, 0), (0, -1, 1), (0, 0, 1), (0, 1, 0), (1, 0, -1)}.

1, 2, 6, 20, 72, 275, 1093, 4479, 18801, 80451, 349700, 1540012, 6856998, 30819381, 139647086, 637238709, 2925903993, 13508063971, 62666934328, 291993695249, 1365865078510, 6411761519748, 30195341581719, 142617094236380, 675403835836741, 3206416193453260, 15256531432328357, 72743764252082951

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, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A122737 A338184 A348351 * A059279 A154381 A150135

Adjacent sequences: A150131 A150132 A150133 * A150135 A150136 A150137

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved