A151070 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), (0, 1, 0), (1, 0, 0), (1, 0, 1)}.

1, 3, 10, 39, 161, 683, 2981, 13314, 60227, 275345, 1272372, 5924933, 27748370, 130690142, 618564321, 2938763011, 14009587697, 67002293485, 321313356800, 1544467776401, 7440257304105, 35913933641154, 173655261735906, 841017573506475, 4079158044680209, 19811469122215936, 96336359743407483

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, k, -1 + n] + aux[i, -1 + j, 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: A005750 A151068 A151069 * A151071 A063022 A371713

Adjacent sequences: A151067 A151068 A151069 * A151071 A151072 A151073

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved