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

1,2

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

Formula

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

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);

Crossrefs

Column k=3 of A309148.

Sequence in context: A020988 A177238 A084480 * A099553 A119694 A286760

Adjacent sequences: A309179 A309180 A309181 * A309183 A309184 A309185

Keyword

nonn

Author

Alois P. Heinz, Jul 15 2019

Status

approved