A282617 - OEIS

%I #20 Mar 23 2017 10:43:38

%S 0,0,0,4,14,104,594,3988,29188,227588,1983482,18398780,188210020,

%T 2030025592,23828759942,293948660282,3909402733418

%N Number of non-self-conjugate inseparable 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) = A282619(n) - A282618(n).

%F a(n) = A202705(n) - A279197(n).

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

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

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

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

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

%Y Cf. A104429, A202705, A279197, A279199, A282615, A282616, A282618, A282619.

%K nonn,more

%O 1,4

%A _Peter Kagey_, Feb 19 2017

%E a(10)-a(16) from _Fausto A. C. Cariboni_, Feb 27 2017

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