A150335 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), (0, 0, 1), (1, 0, 1)}.

1, 2, 7, 23, 84, 320, 1262, 5098, 21051, 87729, 371394, 1584946, 6832849, 29666458, 129708627, 570060258, 2519251688, 11178295951, 49819703001, 222797463880, 999874253662, 4500199157553, 20313008617526, 91912052460063, 416903349368491, 1894989864295280, 8631524632718693, 39387758710865188

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, j, -1 + k, -1 + n] + aux[i, 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: A127497 A151291 A150334 * A150336 A173519 A151292

Adjacent sequences: A150332 A150333 A150334 * A150336 A150337 A150338

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved