A150953 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, 0), (1, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 35, 157, 681, 3184, 14449, 68514, 318868, 1528662, 7224945, 34859918, 166473286, 807330834, 3883821511, 18902679334, 91430966947, 446307098244, 2167781051280, 10605760372222, 51682964710713, 253340097702432, 1237816223983285, 6077025738208497, 29756488885651326, 146285190846706373

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, 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: A150950 A150951 A150952 * A150954 A150955 A150956

Adjacent sequences: A150950 A150951 A150952 * A150954 A150955 A150956

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved