A150686 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, -1), (0, 1, 1), (1, -1, -1), (1, 1, 1)}.

1, 2, 8, 26, 116, 454, 2050, 8794, 39660, 178810, 814012, 3754848, 17342124, 80797170, 378229240, 1774813836, 8382841888, 39623699326, 188152522980, 895426882954, 4269559367648, 20422364667082, 97782086198020, 469341302498804, 2256133502657678, 10859462256974084, 52368606518300482, 252753850113203114

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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 1 + 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: A150683 A150684 A150685 * A150687 A150688 A026660

Adjacent sequences: A150683 A150684 A150685 * A150687 A150688 A150689

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved