A309182 (1/3) times the number of n-member subsets of [3n] whose elements sum to a multiple of n.

1, 2, 10, 42, 201, 1028, 5538, 30666, 173593, 1001402, 5864750, 34769364, 208267320, 1258574116, 7663720710, 46976034378, 289628805623, 1794932294978, 11175157356522, 69864075597442, 438403736549145, 2760351027094300, 17433869214973754, 110420300879752980

Offset: 1

Author

Alois P. Heinz, Jul 15 2019

Keywords

• nonn

Comments

Also (1/2) times the number of n-member subsets of [3n-1] whose elements sum to a multiple of n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Column k=3 of A309148.

Programs

Maple

with(numtheory):
a:= n-> add(binomial(3*d, d)*(-1)^(n+d)*
        phi(n/d), d in divisors(n))/(3*n):
seq(a(n), n=1..25);

Formula

a(n) = 1/(3n) * Sum_{d|n} binomial(3d,d)*(-1)^(n+d)*phi(n/d).