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 A202705 Number of irreducible ways to split 1, 2, 3, ..., 3n into n arithmetic progressions each with 3 terms. 10
 1, 1, 1, 2, 6, 25, 115, 649, 4046, 29674, 228030, 1987700, 18402704, 188255116, 2030067605, 23829298479, 293949166112, 3909410101509 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS "Irreducible" means that there is no j such that the first j of the triples are a partition of 1, ..., 3j. 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 "K". R. J. Nowakowski, Generalizations of the Langford-Skolem problem, M.S. Thesis, Dept. Math., Univ. Calgary, May 1975. [Scanned copy, with permission.] Gives a(0)-a(10). FORMULA G.f. = 1 - 1/g where g is g.f. for A104429. a(n) = A279197(n) + 2*A279198(n) for n>0. 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. Sequence in context: A269484 A014277 A006965 * A058801 A321720 A321186 Adjacent sequences:  A202702 A202703 A202704 * A202706 A202707 A202708 KEYWORD nonn,more AUTHOR N. J. A. Sloane, Dec 26 2011 EXTENSIONS a(11)-a(14) from Alois P. Heinz, Dec 28 2011 a(15)-a(17) from Fausto A. C. Cariboni, Feb 22 2017 STATUS approved

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Last modified May 20 11:16 EDT 2022. Contains 353871 sequences. (Running on oeis4.)