A149979 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, 1, 1), (0, 1, 0), (1, 0, 0), (1, 1, -1)}.

1, 2, 5, 16, 58, 223, 903, 3779, 16193, 70818, 314743, 1416706, 6446429, 29598120, 136933180, 637675007, 2986393015, 14055119005, 66436372277, 315240014710, 1500917562356, 7167968048581, 34326088927797, 164787986590447, 792864539729057, 3822579703261175, 18463793240825038, 89335475803429973

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A184596 A149978 A212263 * A262441 A328296 A300042

Adjacent sequences: A149976 A149977 A149978 * A149980 A149981 A149982

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved