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 A282615 Number of self-conjugate separable solutions of X + Y = 2Z (integer, disjoint triples from {1,2,3,...,3n}). 10
 0, 1, 1, 3, 4, 9, 20, 35, 102, 160, 736, 930, 5972, 6766, 59017, 61814, 671651 (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) = A282616(n) - A279197(n). a(n) = A279199(n) - A282618(n). EXAMPLE For n = 4 the a(4) = 3 solutions are: (10,12,11),(7,9,8),(4,6,5),(1,3,2), (10,12,11),(5,9,7),(4,8,6),(1,3,2), and (8,12,10),(7,11,9),(2,6,4),(1,5,3). CROSSREFS Cf. A104429, A202705, A279197, A279199, A282616, A282617, A282618, A282619. All of A279197, A279198, A202705, A279199, A104429, A282615 are concerned with counting solutions to X+Y=2Z in various ways. Sequence in context: A291532 A110810 A247579 * A049978 A324764 A092763 Adjacent sequences:  A282612 A282613 A282614 * A282616 A282617 A282618 KEYWORD nonn,more AUTHOR Peter Kagey, Feb 19 2017 EXTENSIONS a(11)-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 June 21 06:55 EDT 2021. Contains 345358 sequences. (Running on oeis4.)