A282618 Number of non-self-conjugate separable solutions of X + Y = 2Z (integer, disjoint triples from {1,2,3,...,3n}).

0, 0, 2, 6, 26, 108, 492, 2562, 14790, 98874, 720614, 5908394, 52572682, 516141316, 5422012074, 61889630476, 749456000504, 9767057565198, 134007980469502, 1958535740848524

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 = 3 the a(3) = 2 solutions are:
(5,9,7),(4,8,6),(1,3,2), and
(7,9,8),(2,6,4),(1,5,3).
		

Crossrefs

Cf. A104429, A202705, A279197, A279199, A282615, A282616, A282617, A282619.

Formula

a(n) = A282619(n) - A282617(n).

a(n) = A279199(n) - A282615(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(20) from Martin Fuller, Jul 15 2025