A282617 Number of non-self-conjugate inseparable solutions of X + Y = 2Z (integer, disjoint triples from {1,2,3,...,3n}).

0, 0, 0, 4, 14, 104, 594, 3988, 29188, 227588, 1983482, 18398780, 188210020, 2030025592, 23828759942, 293948660282, 3909402733418, 54360500959634, 806312590045382

Offset: 1

Author

Peter Kagey, Feb 19 2017

Keywords

• nonn
• more

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 |

Examples

			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.

Formula

a(n) = A282619(n) - A282618(n).

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

Extensions

a(10)-a(16) from Fausto A. C. Cariboni, Feb 27 2017

a(17) from Fausto A. C. Cariboni, Mar 22 2017

a(18)-a(19) from Martin Fuller, Jul 15 2025