A149673 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, 1), (0, -1, 1), (0, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 65, 255, 1051, 4337, 18319, 77799, 335201, 1450767, 6335303, 27779333, 122569423, 542725045, 2414192351, 10771535425, 48230144207, 216516379107, 974747732287, 4398144695763, 19891097561473, 90135432973947, 409245946151499, 1861292534594845, 8479599885242863, 38689127745452473

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, 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, -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: A195531 A273535 A149672 * A046231 A092896 A149674

Adjacent sequences: A149670 A149671 A149672 * A149674 A149675 A149676

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved