A150958 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), (1, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 35, 161, 703, 3308, 15122, 72146, 337554, 1624538, 7708209, 37313224, 178711601, 868676024, 4188241305, 20421625766, 98946491428, 483640505326, 2352183939670, 11520059367790, 56194856236216, 275672434754150, 1347969330500357, 6621840929151330, 32443366067357835, 159566046988282926

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, -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: A150956 A151309 A150957 * A150959 A150960 A150961

Adjacent sequences: A150955 A150956 A150957 * A150959 A150960 A150961

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved