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%I A202705 #43 Apr 10 2017 00:04:03
%S A202705 1,1,1,2,6,25,115,649,4046,29674,228030,1987700,18402704,188255116,
%T A202705 2030067605,23829298479,293949166112,3909410101509
%N A202705 Number of irreducible ways to split 1, 2, 3, ..., 3n into n arithmetic progressions each with 3 terms.
%C A202705 "Irreducible" means that there is no j such that the first j of the triples are a partition of 1, ..., 3j.
%D A202705 R. K. Guy, Sedlacek's Conjecture on Disjoint Solutions of x+y= z, Univ. Calgary, Dept. Mathematics, Research Paper No. 129, 1971.
%D A202705 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 A202705 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 A202705 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 "K".
%H A202705 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.] Gives a(0)-a(10).
%F A202705 G.f. = 1 - 1/g where g is g.f. for A104429.
%F A202705 a(n) = A279197(n) + 2*A279198(n) for n>0.
%Y A202705 All of A279197, A279198, A202705, A279199, A104429, A282615 are concerned with counting solutions to X+Y=2Z in various ways.
%Y A202705 See also A002848, A002849.
%K A202705 nonn,more
%O A202705 0,4
%A A202705 _N. J. A. Sloane_, Dec 26 2011
%E A202705 a(11)-a(14) from _Alois P. Heinz_, Dec 28 2011
%E A202705 a(15)-a(17) from _Fausto A. C. Cariboni_, Feb 22 2017

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