A148866 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, 0, 0), (0, 0, 1), (1, -1, 1), (1, 0, -1), (1, 1, -1)}.

1, 1, 3, 8, 28, 98, 374, 1450, 5853, 24018, 100685, 427876, 1843316, 8023328, 35263612, 156234952, 697236891, 3131311800, 14143354394, 64206790059, 292826696557, 1341068890771, 6165144306416, 28441036921835, 131624562270991, 610953509983029, 2843566203006533, 13268357936674289, 62057350259243755

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A203152 A362645 A026627 * A327015 A151431 A245892

Adjacent sequences: A148863 A148864 A148865 * A148867 A148868 A148869

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved