%I #26 Mar 23 2017 11:56:36

%S 0,1,1,3,4,9,20,35,102,160,736,930,5972,6766,59017,61814,671651

%N Number of self-conjugate separable solutions of X + Y = 2Z (integer, disjoint triples from {1,2,3,...,3n}).

%C An inseparable solution is one in which "there is no j such that the first j of the triples are a partition of 1, ..., 3j" (see A202705).

%C A self-conjugate solution is one in which for every triple (a, b, c) in the partition there exists a "conjugate" triple (m-a, m-b, m-c) or (m-b, m-a, m-c) where m = 3n+1.

%C | separable | inseparable | either |

%C -------------------+-----------+-------------+---------+

%C self-conjugate | A282615 | A279197 | A282616 |

%C non-self-conjugate | A282618 | A282617 | A282619 |

%C either | A279199 | A202705 | A104429 |

%F a(n) = A282616(n) - A279197(n).

%F a(n) = A279199(n) - A282618(n).

%e For n = 4 the a(4) = 3 solutions are:

%e (10,12,11),(7,9,8),(4,6,5),(1,3,2),

%e (10,12,11),(5,9,7),(4,8,6),(1,3,2), and

%e (8,12,10),(7,11,9),(2,6,4),(1,5,3).

%Y Cf. A104429, A202705, A279197, A279199, A282616, A282617, A282618, A282619.

%Y All of A279197, A279198, A202705, A279199, A104429, A282615 are concerned with counting solutions to X+Y=2Z in various ways.

%K nonn,more

%O 1,4

%A _Peter Kagey_, Feb 19 2017

%E a(11)-a(16) from _Fausto A. C. Cariboni_, Feb 27 2017

%E a(17) from _Fausto A. C. Cariboni_, Mar 22 2017