A318431 Number of n-element subsets of [3n] whose elements sum to a multiple of n.

1, 3, 6, 30, 126, 603, 3084, 16614, 91998, 520779, 3004206, 17594250, 104308092, 624801960, 3775722348, 22991162130, 140928103134, 868886416869, 5384796884934, 33525472069566, 209592226792326, 1315211209647435, 8281053081282900, 52301607644921262

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Marko Riedel et al., Number of n-element subsets divisible by n

Formula

a(n) = (-1)^n * (1/n) * Sum_{d|n} C(3d,d)*(-1)^d*phi(n/d) for n>0, a(0)=1.

Maple

with(numtheory); a := n -> `if`(n=0, 1, (-1)^n * 1/n * add(binomial(3*d, d)*(-1)^d*phi(n/d), d in divisors(n)));

Prog

(PARI) a(n) = if (n, (-1)^n * (1/n) * sumdiv(n, d, binomial(3*d, d)*(-1)^d*eulerphi(n/d)), 1); \\ Michel Marcus, Aug 27 2018

Crossrefs

Cf. A169888, A318432, A318433.

Column k=3 of A304482.

Sequence in context: A361864 A280981 A265376 * A157534 A372024 A133799

Adjacent sequences: A318428 A318429 A318430 * A318432 A318433 A318434

Keyword

nonn

Author

Marko Riedel, Aug 26 2018

Status

approved