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Number of ways to write n as an ordered sum of 3 nonprime numbers.
9

%I #10 Feb 21 2021 20:55:58

%S 1,0,0,3,0,3,3,3,9,4,9,12,12,15,21,19,27,30,30,39,42,46,54,60,61,75,

%T 72,91,90,108,99,129,123,142,147,168,156,201,180,217,213,246,235,279,

%U 255,304,297,336,327,375,342,412,390,447,423,492,453,529,507,573,538,630,579

%N Number of ways to write n as an ordered sum of 3 nonprime numbers.

%H Robert Israel, <a href="/A341480/b341480.txt">Table of n, a(n) for n = 3..10000</a>

%F G.f. g(x)^3 where g(x) is the G.f. of A005171.

%p b:= proc(n, t) option remember;

%p `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(

%p `if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))

%p end:

%p a:= n-> b(n, 3):

%p seq(a(n), n=3..65); # _Alois P. Heinz_, Feb 13 2021

%t nmax = 65; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^3, {x, 0, nmax}], x] // Drop[#, 3] &

%Y Cf. A005171, A018252, A052284, A076608, A098238, A341408, A341461, A341481, A341482, A341483, A341484, A341485, A341486.

%K nonn

%O 3,4

%A _Ilya Gutkovskiy_, Feb 13 2021