A150607 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, 0, -1), (1, 0, 1)}.

1, 2, 7, 27, 111, 471, 2070, 9205, 41712, 190680, 880088, 4092508, 19136861, 89985447, 424886474, 2013955551, 9578423131, 45684653123, 218478608672, 1047225553291, 5030175331878, 24207638670055, 116697391967049, 563452054918905, 2724424172511156, 13190686863809458, 63942816664278943

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, j, -1 + k, -1 + n] + aux[-1 + i, 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: A150604 A150605 A150606 * A150608 A150609 A150610

Adjacent sequences: A150604 A150605 A150606 * A150608 A150609 A150610

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved