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A309561 Total sum of prime parts in all compositions of n. 2
0, 0, 2, 7, 16, 44, 102, 244, 554, 1247, 2772, 6111, 13334, 28916, 62302, 133557, 285020, 605869, 1283362, 2710008, 5706546, 11986171, 25118500, 52529339, 109643310, 228455907, 475250388, 987177924, 2047710144, 4242128909, 8777675002, 18142184432, 37458037658 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..3312

FORMULA

G.f.: Sum_{k>=1} prime(k)*x^prime(k)*(1-x)^2/(1-2*x)^2.

a(n) ~ c * 2^n * n, where c = 0.27326606442562679135064648817419092073886899135... - Vaclav Kotesovec, Aug 18 2019

EXAMPLE

a(4) = 16: 1111, (2)11, 1(2)1, 11(2), (2)(2), (3)1, 1(3), 4.

MAPLE

a:= proc(n) option remember; add(a(n-j) +j*

      `if`(isprime(j), ceil(2^(n-j-1)), 0), j=1..n)

    end:

seq(a(n), n=0..33);

CROSSREFS

Cf. A000040, A001787, A073118, A102291.

Sequence in context: A073371 A113224 A178945 * A026571 A100099 A164267

Adjacent sequences:  A309558 A309559 A309560 * A309562 A309563 A309564

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 07 2019

STATUS

approved

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Last modified December 15 11:43 EST 2019. Contains 329999 sequences. (Running on oeis4.)