A150469 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, 0, 0), (0, -1, 1), (0, 1, 0), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 25, 98, 403, 1707, 7426, 32894, 147944, 673326, 3094753, 14342117, 66924879, 314151068, 1482168472, 7023972680, 33415868060, 159517768182, 763809202239, 3667224010284, 17650041654131, 85134332930215, 411456500913167, 1992159854549999, 9661315838754195, 46924453840350756, 228222827414791021

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150466 A150467 A150468 * A150470 A150471 A150472

Adjacent sequences: A150466 A150467 A150468 * A150470 A150471 A150472

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved