A150057 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, -1, 1), (-1, 0, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 6, 18, 63, 217, 822, 3042, 12073, 46756, 191331, 764383, 3196583, 13064986, 55529435, 230948432, 994032777, 4191650602, 18224285458, 77714819878, 340690355325, 1466403984890, 6473061148864, 28081108273621, 124685793447785, 544555483915367, 2430162878129049, 10675588779615415

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, k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A204686 A098964 A079469 * A150058 A150059 A150060

Adjacent sequences: A150054 A150055 A150056 * A150058 A150059 A150060

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved