A148199 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, 1), (1, -1, 0), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 12, 33, 109, 342, 1226, 4201, 15742, 57080, 221634, 837409, 3332844, 12983589, 52719344, 210307546, 867369706, 3526066972, 14731903807, 60815029670, 256818485041, 1073752848245, 4575811278716, 19337011492356, 83048998903207, 354171226561322, 1531417121693314, 6582338524938034

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, 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: A148196 A148197 A148198 * A343663 A377101 A108530

Adjacent sequences: A148196 A148197 A148198 * A148200 A148201 A148202

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved