This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A202705 #49 Jul 08 2025 10:46:26 %S A202705 1,1,1,2,6,25,115,649,4046,29674,228030,1987700,18402704,188255116, %T A202705 2030067605,23829298479,293949166112,3909410101509,54360507919179, %U A202705 806312701922676 %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.: 2 - 1/g where g is g.f. for A104429. [corrected by _Martin Fuller_, Jul 08 2025] %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 %E A202705 a(18)-a(19) from _Martin Fuller_, Jul 08 2025