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A309182 (1/3) times the number of n-member subsets of [3n] whose elements sum to a multiple of n. 2
1, 2, 10, 42, 201, 1028, 5538, 30666, 173593, 1001402, 5864750, 34769364, 208267320, 1258574116, 7663720710, 46976034378, 289628805623, 1794932294978, 11175157356522, 69864075597442, 438403736549145, 2760351027094300, 17433869214973754, 110420300879752980 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 19 14:43 EDT 2019. Contains 327198 sequences. (Running on oeis4.)