A282616 Number of self-conjugate solutions of X + Y = 2Z (integer, disjoint triples from {1,2,3,...,3n}).

1, 2, 3, 5, 15, 20, 75, 93, 588, 602, 4954, 4854, 51068, 48779, 597554, 567644, 8039742, 7634924, 120721322, 114398957, 2017517155, 1889828995, 36749338386, 34451341024, 726198499999, 679116640274, 15459385244039, 14509756794668, 356501015466981, 332645434167718, 8701627694048482

Offset

1,2

Comments

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

Table of n, a(n) for n=1..31.

Formula

a(n) = A282615(n) + A279197(n).

a(n) = A104429(n) - A282619(n).

Example

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

Crossrefs

Cf. A104429, A202705, A279197, A279199, A282615, A282617, A282618, A282619.

Sequence in context: A099410 A330988 A102033 * A174418 A072246 A292903

Adjacent sequences: A282613 A282614 A282615 * A282617 A282618 A282619

Keyword

nonn

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

a(18)-a(24) from Bert Dobbelaere, May 29 2025

a(25)-a(31) from Martin Fuller, Jul 15 2025

Status

approved