A150940 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, 0), (1, 0, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 34, 158, 679, 3259, 14778, 72035, 336351, 1652756, 7856265, 38791109, 186570598, 924127805, 4481227016, 22244859809, 108510762260, 539484498647, 2643340780016, 13156928004175, 64686223962835, 322245205614827, 1588570700484800, 7918963752318771, 39121529493071983, 195120227989560344

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A150938 A151307 A150939 * A150941 A150942 A150943

Adjacent sequences: A150937 A150938 A150939 * A150941 A150942 A150943

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved