A150017 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, 0, 0)}.

1, 2, 5, 18, 66, 244, 969, 3910, 15996, 66897, 282755, 1207481, 5203126, 22601356, 98848043, 434437333, 1920624701, 8530573178, 38019148241, 170151483827, 764088116366, 3440559265944, 15538126966380, 70357813200780, 319292984904688, 1452158198124916, 6618445538244401, 30219910831230542

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, k, -1 + 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: A150014 A150015 A150016 * A150018 A150019 A005753

Adjacent sequences: A150014 A150015 A150016 * A150018 A150019 A150020

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved