

A317577


Number of ways the set {1,2,...,n} can be split into three subsets X, Y, Z of equal sums, where the order of X, Y, Z matters.


0



0, 0, 0, 0, 6, 6, 0, 18, 54, 0, 258, 612, 0, 3570, 8880, 0, 55764, 142368, 0, 947946, 2468844, 0, 17099808, 45375498, 0, 323927184, 871038570, 0, 6369199908, 17312303760
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OFFSET

1,5


COMMENTS

Constant term of Product_{k=1..n} (x^k+y^k+1/(x*y)^k).


LINKS

Table of n, a(n) for n=1..30.
D. Andrica and O. Bagdasar, Some remarks on 3partitions of multisets, Electron. Notes Discrete Math., TCDM'18 (2018).


FORMULA

a(n) = 6*A112972(n).


EXAMPLE

For n = 1, 2, 3, 4, a(n) = 0, as n*(n+1)/2 is not divisible by 3.
For n = 5, a(5) = 6, as {1,2,3,4,5} = {1,4}U{2,3}U{5} and there are 6 permutations.
For n = 6, a(6) = 6, as {1,2,3,4,5,6} = {1,6}U{2,5}U{3,4} and there are 6 permutations.


CROSSREFS

Cf. A112972.
Sequence in context: A153629 A154155 A021942 * A245173 A256273 A046620
Adjacent sequences: A317574 A317575 A317576 * A317578 A317579 A317580


KEYWORD

nonn,easy


AUTHOR

Ovidiu Bagdasar, Jul 31 2018


STATUS

approved



