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 A282617 Number of non-self-conjugate inseparable solutions of X + Y = 2Z (integer, disjoint triples from {1,2,3,...,3n}). 5
 0, 0, 0, 4, 14, 104, 594, 3988, 29188, 227588, 1983482, 18398780, 188210020, 2030025592, 23828759942, 293948660282, 3909402733418 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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). 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.                    | separable | inseparable | either  | -------------------+-----------+-------------+---------+ self-conjugate     | A282615   | A279197     | A282616 | non-self-conjugate | A282618   | A282617     | A282619 | either             | A279199   | A202705     | A104429 | LINKS FORMULA a(n) = A282619(n) - A282618(n). a(n) = A202705(n) - A279197(n). EXAMPLE For n = 4 the a(4) = 4 solutions are: (7,11,9),(4,12,8),(2,10,6),(1,5,3), (9,11,10),(4,8,6),(2,12,7),(1,5,3), (8,12,10),(3,11,7),(2,6,4),(1,9,5), and (8,12,10),(5,9,7),(2,4,3),(1,11,6). CROSSREFS Cf. A104429, A202705, A279197, A279199, A282615, A282616, A282618, A282619. Sequence in context: A299199 A209322 A110302 * A005743 A343962 A283793 Adjacent sequences:  A282614 A282615 A282616 * A282618 A282619 A282620 KEYWORD nonn,more AUTHOR Peter Kagey, Feb 19 2017 EXTENSIONS a(10)-a(16) from Fausto A. C. Cariboni, Feb 27 2017 a(17) from Fausto A. C. Cariboni, Mar 22 2017 STATUS approved

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Last modified May 20 11:16 EDT 2022. Contains 353871 sequences. (Running on oeis4.)