

A104429


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


38



1, 1, 2, 5, 15, 55, 232, 1161, 6643, 44566, 327064, 2709050, 24312028, 240833770, 2546215687, 29251369570, 355838858402, 4658866773664
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OFFSET

0,3


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. 221223.
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. 173179, 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 "M".
R. J. Nowakowski, Generalizations of the LangfordSkolem problem, M.S. Thesis, Dept. Math., Univ. Calgary, May 1975. [Scanned copy, with permission.] Gives a(0)a(10).


EXAMPLE

{{{1,2,3},{4,5,6},{7,8,9}}, {{1,2,3},{4,6,8},{5,7,9}}, {{1,3,5},{2,4,6},{7,8,9}}, {{1,4,7},{2,5,8},{3,6,9}}, {{1,5,9},{2,3,4},{6,7,8}}} are the 5 ways to split 1, 2, 3, ..., 9 into 3 arithmetic progressions each with 3 elements. Thus a(3)=5.


CROSSREFS

Cf. A104430A104443.
All of A279197, A279198, A202705, A279199, A282615 are concerned with counting solutions to X+Y=2Z in various ways.
See also A002848, A002849, A334250.
Sequence in context: A051295 A334154 A009383 * A109319 A059219 A242275
Adjacent sequences: A104426 A104427 A104428 * A104430 A104431 A104432


KEYWORD

nonn,nice,more


AUTHOR

Jonas Wallgren, Mar 17 2005


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



