A149229 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), (-1, 1, 1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 10, 46, 146, 700, 2492, 12157, 46188, 227311, 900226, 4452740, 18148307, 90047902, 374826004, 1863659513, 7883484889, 39253107698, 168170902251, 838196417310, 3628259977798, 18097238940635, 79007013608333, 394289893216477, 1733728245047414, 8655824582343977, 38293785863624445

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + 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: A184481 A149227 A149228 * A149230 A115327 A233395

Adjacent sequences: A149226 A149227 A149228 * A149230 A149231 A149232

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved