A150251 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, 0), (0, 1, 1), (1, 0, -1), (1, 0, 0)}.

1, 2, 6, 22, 85, 340, 1411, 6036, 26163, 114983, 513060, 2308456, 10465788, 47829991, 219922058, 1016135334, 4717666738, 21999886908, 102949227180, 483335249790, 2276438144176, 10750317622193, 50890349439787, 241472604286962, 1148196982158353, 5469920809676455, 26105092657585897, 124796430590276424

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, 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: A105871 A150249 A150250 * A150252 A150253 A150254

Adjacent sequences: A150248 A150249 A150250 * A150252 A150253 A150254

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved