A202705 Number of irreducible ways to split 1, 2, 3, ..., 3n into n arithmetic progressions each with 3 terms.

1, 1, 1, 2, 6, 25, 115, 649, 4046, 29674, 228030, 1987700, 18402704, 188255116, 2030067605, 23829298479, 293949166112, 3909410101509

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

Table of n, a(n) for n=0..17.

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 A358499

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