A149743 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), (0, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 77, 317, 1417, 6371, 29019, 134117, 623759, 2923269, 13791533, 65305615, 310841939, 1483967601, 7107996949, 34140691615, 164350687661, 792968518081, 3832938906141, 18559199721669, 90004738169245, 437085667023033, 2125372248538213, 10346780105421687, 50424759540183311, 245988413963497411

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[-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, 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: A149740 A149741 A149742 * A323794 A151479 A330800

Adjacent sequences: A149740 A149741 A149742 * A149744 A149745 A149746

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved