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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).

%I A279199 #36 Jul 08 2025 07:47:11
%S A279199 0,0,1,3,9,30,117,512,2597,14892,99034,721350,5909324,52578654,
%T A279199 516148082,5422071091,61889692290,749456672155,9767058240577,
%U A279199 134007989313530,1958535749524107
%N 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).
%D A279199 R. K. Guy, Sedlacek's Conjecture on Disjoint Solutions of x+y= z, Univ. Calgary, Dept. Mathematics, Research Paper No. 129, 1971.
%D A279199 R. K. Guy, Sedlacek's Conjecture on Disjoint Solutions of x+y= z, in Proc. Conf. Number Theory. Pullman, WA, 1971, pp. 221-223.
%D A279199 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.
%H A279199 R. K. Guy, Letter to N. J. A. Sloane, June 24 1971: <a href="/A002572/a002572.jpg">front</a>, <a href="/A002572/a002572_1.jpg">back</a> [Annotated scanned copy, with permission] See sequence "L".
%H A279199 R. J. Nowakowski, <a href="/A104429/a104429.pdf">Generalizations of the Langford-Skolem problem</a>, M.S. Thesis, Dept. Math., Univ. Calgary, May 1975. [Scanned copy, with permission.]
%F A279199 a(n) = A104429(n)-A202705(n) = Sum_{i=1..n-1} A104429(i)*A202705(n-i). - _Martin Fuller_, Jul 08 2025
%Y A279199 All of A279197, A279198, A202705, A279199, A104429, A282615 are concerned with counting solutions to X+Y=2Z in various ways.
%Y A279199 See also A002848, A002849.
%K A279199 nonn,more
%O A279199 0,4
%A A279199 _N. J. A. Sloane_, Dec 15 2016
%E A279199 Definition corrected by _N. J. A. Sloane_, Jan 09 2017 at the suggestion of _Fausto A. C. Cariboni_.
%E A279199 a(15)-a(17) from _Fausto A. C. Cariboni_, Feb 22 2017
%E A279199 a(18)-a(20) from _Martin Fuller_, Jul 08 2025