A149243 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), (-1, 1, 1), (0, 0, -1), (1, 0, 1)}.

1, 1, 4, 11, 36, 125, 453, 1643, 6188, 23609, 91127, 355475, 1402336, 5573671, 22297494, 89782237, 363634796, 1479469837, 6045872801, 24810245469, 102175595798, 422157858039, 1749638392988, 7271801874529, 30300634687428, 126561757177773, 529820253495847, 2222601036368867, 9341909964352610

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, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + 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: A149240 A149241 A149242 * A112849 A372721 A149244

Adjacent sequences: A149240 A149241 A149242 * A149244 A149245 A149246

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved