A104185 Number of partitions of the set {1, 2, 3, ..., 6n+3} into 2n+1 sets of 3 elements each, such that each 3-element set has the same sum (there are no such partitions unless there are 6n+3 elements).

1, 2, 11, 84, 1296, 24293, 703722, 24212879, 1157746949, 63552536107, 4553087575565, 364552628480443

Offset

0,2

References

Dossey, Giordano, McCrone and Weir, Mathematics methods and modeling for today's mathematics classroom, p. 134.

Links

Table of n, a(n) for n=0..11.

Michael Paul Goldenberg, Online discussion

Example

a(1) = 2 because with 9 elements they can be partitioned (9 5 1) (8 4 3) (7 6 2) or (9 4 2) (8 6 1) (7 5 3).

Prog

(Scheme) ; Program to generate terms of the sequence available from Joshua Zucker on request.

Crossrefs

Bisection of column k=3 of A203986. - Alois P. Heinz, Jan 09 2012

Sequence in context: A379189 A086406 A158098 * A074604 A135404 A370475

Adjacent sequences: A104182 A104183 A104184 * A104186 A104187 A104188

Keyword

more,nonn

Author

Joshua Zucker, Mar 11 2005

Extensions

More terms from Guenter Stertenbrink

The terms 1157746949, 63552536107 were found by Don Knuth, Sep 04 2009

a(10)-a(11) from Martin Fuller, Jan 21 2026

Status

approved