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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 (list; graph; refs; listen; history; text; internal format)
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 3-partitions 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

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Last modified August 13 19:30 EDT 2020. Contains 336451 sequences. (Running on oeis4.)