A148453 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, 0), (0, 0, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 2, 6, 17, 53, 181, 629, 2273, 8442, 31903, 123276, 482016, 1909749, 7671004, 31041259, 126847637, 522862741, 2167729171, 9053158292, 38026043662, 160503188086, 681190257778, 2902953020464, 12422813296300, 53381627069382, 230129554758325, 995583076288227, 4320678366122981

Offset

0,3

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A367056 A368598 A346428 * A097514 A108630 A338735

Adjacent sequences: A148450 A148451 A148452 * A148454 A148455 A148456

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved