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%I A282617 #20 Mar 23 2017 10:43:38
%S A282617 0,0,0,4,14,104,594,3988,29188,227588,1983482,18398780,188210020,
%T A282617 2030025592,23828759942,293948660282,3909402733418
%N A282617 Number of non-self-conjugate inseparable solutions of X + Y = 2Z (integer, disjoint triples from {1,2,3,...,3n}).
%C A282617 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 A282617 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 A282617                    | separable | inseparable | either  |
%C A282617 -------------------+-----------+-------------+---------+
%C A282617 self-conjugate     | A282615   | A279197     | A282616 |
%C A282617 non-self-conjugate | A282618   | A282617     | A282619 |
%C A282617 either             | A279199   | A202705     | A104429 |
%F A282617 a(n) = A282619(n) - A282618(n).
%F A282617 a(n) = A202705(n) - A279197(n).
%e A282617 For n = 4 the a(4) = 4 solutions are:
%e A282617 (7,11,9),(4,12,8),(2,10,6),(1,5,3),
%e A282617 (9,11,10),(4,8,6),(2,12,7),(1,5,3),
%e A282617 (8,12,10),(3,11,7),(2,6,4),(1,9,5), and
%e A282617 (8,12,10),(5,9,7),(2,4,3),(1,11,6).
%Y A282617 Cf. A104429, A202705, A279197, A279199, A282615, A282616, A282618, A282619.
%K A282617 nonn,more
%O A282617 1,4
%A A282617 _Peter Kagey_, Feb 19 2017
%E A282617 a(10)-a(16) from _Fausto A. C. Cariboni_, Feb 27 2017
%E A282617 a(17) from _Fausto A. C. Cariboni_, Mar 22 2017

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