A148359 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, 1, -1), (0, 0, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 2, 5, 15, 45, 155, 542, 1966, 7466, 28640, 112818, 452793, 1838031, 7579723, 31599165, 132977936, 565343035, 2421524022, 10449677575, 45409673570, 198464619163, 872445045025, 3854836942828, 17111520704731, 76299963048366, 341577472122899, 1534985507846434, 6922480431094339

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, -1 + j, 1 + 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: A148358 A149913 A065848 * A287582 A122392 A139782

Adjacent sequences: A148356 A148357 A148358 * A148360 A148361 A148362

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved