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A309128 (1/n) times the sum of the elements of all subsets of [n] whose sum is divisible by n. 3
1, 1, 4, 4, 12, 20, 40, 70, 150, 284, 564, 1116, 2212, 4392, 8768, 17404, 34704, 69214, 137980, 275264, 549340, 1096244, 2188344, 4369196, 8724196, 17422500, 34797476, 69505628, 138845940, 277383904, 554189344, 1107296248, 2212559996, 4421289872, 8835361488 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

Conjecture: a(n) = (n + 1) * A063776(n)/4 - (phi(n)/2) * (1 + (-1)^n)/2 = ((n + 1)/(4*n)) * A053636(n) - (phi(n)/2) * (1 + (-1)^n)/2. - Petros Hadjicostas, Jul 20 2019

a(n) = A309280(n,n). - Alois P. Heinz, Jul 21 2019

EXAMPLE

The subsets of [5] whose sum is divisible by 5 are: {}, {5}, {1,4}, {2,3}, {1,4,5}, {2,3,5}, {1,2,3,4}, {1,2,3,4,5}.  The sum of their elements is 0 + 5 + 5 + 5 + 10 + 10 + 10 + 15 = 60.  So a(5) = 60/5 = 12.

MAPLE

b:= proc(n, m, s) option remember; `if`(n=0, [`if`(s=0, 1, 0), 0],

      b(n-1, m, s) +(g-> g+[0, g[1]*n])(b(n-1, m, irem(s+n, m))))

    end:

a:= proc(n) option remember; forget(b); b(n$2, 0)[2]/n end:

seq(a(n), n=1..40);

CROSSREFS

Cf. A000010, A001792 (the same for all subsets), A053636, A063776, A309122, A309280.

Sequence in context: A303315 A331606 A079902 * A120033 A097073 A019085

Adjacent sequences:  A309125 A309126 A309127 * A309129 A309130 A309131

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 13 2019

STATUS

approved

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Last modified September 24 08:13 EDT 2021. Contains 347623 sequences. (Running on oeis4.)