A150063 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, 0, 0), (0, 1, 0), (1, -1, -1), (1, 1, 0)}.

1, 2, 6, 18, 63, 226, 864, 3353, 13492, 55230, 230555, 973313, 4164492, 18014395, 78699792, 346360582, 1534976053, 6847432097, 30734846866, 138669026551, 628473868348, 2860412709280, 13072048003935, 59962382560696, 275961424663957, 1273860736450060, 5897122781889323, 27374352773426976

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, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, 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: A150060 A150061 A150062 * A150064 A148463 A150065

Adjacent sequences: A150060 A150061 A150062 * A150064 A150065 A150066

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved