A149695 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, 0), (0, 0, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 17, 67, 283, 1215, 5229, 23539, 105631, 478363, 2203783, 10170875, 47141319, 220757939, 1035081113, 4868748935, 23045709931, 109220598807, 518814819579, 2474927856303, 11819069398291, 56541537527071, 271302979227019, 1303029745268783, 6266958272900963, 30207948281148719, 145729084024706419

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A149692 A149693 A149694 * A162270 A146790 A149696

Adjacent sequences: A149692 A149693 A149694 * A149696 A149697 A149698

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved