A279199 Number of reducible ways to split 1, 2, 3, ..., 3n into n arithmetic progressions each with 3 terms: a(n) = A104429(n) - A202705(n).

0, 0, 1, 3, 9, 30, 117, 512, 2597, 14892, 99034, 721350, 5909324, 52578654, 516148082, 5422071091, 61889692290, 749456672155, 9767058240577, 134007989313530, 1958535749524107

Offset: 0

Author

N. J. A. Sloane, Dec 15 2016

Keywords

• nonn
• more

References

• R. K. Guy, Sedlacek's Conjecture on Disjoint Solutions of x+y= z, Univ. Calgary, Dept. Mathematics, Research Paper No. 129, 1971.
• R. K. Guy, Sedlacek's Conjecture on Disjoint Solutions of x+y= z, in Proc. Conf. Number Theory. Pullman, WA, 1971, pp. 221-223.
• R. K. Guy, Packing [1,n] with solutions of ax + by = cz; the unity of combinatorics, in Colloq. Internaz. Teorie Combinatorie. Rome, 1973, Atti Conv. Lincei. Vol. 17, Part II, pp. 173-179, 1976.

Links

• R. K. Guy, Letter to N. J. A. Sloane, June 24 1971: front, back [Annotated scanned copy, with permission] See sequence "L".
• R. J. Nowakowski, Generalizations of the Langford-Skolem problem, M.S. Thesis, Dept. Math., Univ. Calgary, May 1975. [Scanned copy, with permission.]

Crossrefs

All of A279197, A279198, A202705, A279199, A104429, A282615 are concerned with counting solutions to X+Y=2Z in various ways.

See also A002848, A002849.

Formula

a(n) = A104429(n)-A202705(n) = Sum_{i=1..n-1} A104429(i)*A202705(n-i). - Martin Fuller, Jul 08 2025

Extensions

Definition corrected by N. J. A. Sloane, Jan 09 2017 at the suggestion of Fausto A. C. Cariboni.

a(15)-a(17) from Fausto A. C. Cariboni, Feb 22 2017

a(18)-a(20) from Martin Fuller, Jul 08 2025