A149510 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), (-1, 0, 1), (0, -1, -1), (1, 1, 1)}.

1, 1, 5, 11, 47, 155, 589, 2243, 8561, 33467, 133517, 529315, 2148221, 8691577, 35431673, 145777825, 600472755, 2488691561, 10353202637, 43132961113, 180596954251, 757853615215, 3188079252033, 13450531998057, 56826331572443, 240626394752241, 1021097344594587, 4339536786320825

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, -1 + k, -1 + n] + aux[i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A149507 A149508 A149509 * A149511 A149512 A149513

Adjacent sequences: A149507 A149508 A149509 * A149511 A149512 A149513

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved