A149238 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, -1), (-1, 0, 0), (0, -1, 1), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 11, 36, 125, 435, 1595, 5954, 22465, 86223, 334795, 1315848, 5206019, 20773532, 83318857, 336730400, 1367649633, 5578371219, 22851417683, 93958046678, 387906668755, 1606184507258, 6669799558525, 27769835689296, 115931233180053, 485172793681327, 2034581806716141, 8549095477414610

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A109268 A256960 A174993 * A149239 A149240 A149241

Adjacent sequences: A149235 A149236 A149237 * A149239 A149240 A149241

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved