A150029 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, 1), (1, 0, 0), (1, 0, 1)}.

1, 2, 6, 16, 56, 176, 632, 2080, 7744, 26752, 100352, 353024, 1345280, 4843008, 18516864, 67305984, 259601408, 956426240, 3695605760, 13696663552, 53218287616, 198990118912, 774023897088, 2905880100864, 11346564612096, 42864799645696, 167495532347392, 634607654010880, 2486700816072704

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A147919 A320805 A354083 * A221841 A068787 A073959

Adjacent sequences: A150026 A150027 A150028 * A150030 A150031 A150032

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved