

A282615


Number of selfconjugate 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
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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 selfconjugate solution is one in which for every triple (a, b, c) in the partition there exists a "conjugate" triple (ma, mb, mc) or (mb, ma, mc) where m = 3n+1.
 separable  inseparable  either 
++++
selfconjugate  A282615  A279197  A282616 
nonselfconjugate  A282618  A282617  A282619 
either  A279199  A202705  A104429 


LINKS

Table of n, a(n) for n=1..17.


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



