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A341481 Number of ways to write n as an ordered sum of 4 nonprime numbers.

%I A341481 #10 Feb 21 2021 20:56:03
%S A341481 1,0,0,4,0,4,6,4,16,8,18,28,25,40,50,56,76,92,98,136,147,176,212,240,
%T A341481 272,328,352,420,471,524,592,668,747,808,938,996,1127,1232,1354,1456,
%U A341481 1658,1720,1966,2052,2279,2408,2700,2772,3144,3232,3568,3740,4117,4228,4722
%N A341481 Number of ways to write n as an ordered sum of 4 nonprime numbers.
%H A341481 Robert Israel, <a href="/A341481/b341481.txt">Table of n, a(n) for n = 4..10000</a>
%F A341481 G.f. g(x)^4, where g(x) is the G.f. of A005171.
%p A341481 b:= proc(n, t) option remember;
%p A341481       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p A341481       `if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))
%p A341481     end:
%p A341481 a:= n-> b(n, 4):
%p A341481 seq(a(n), n=4..58);  # _Alois P. Heinz_, Feb 13 2021
%t A341481 nmax = 58; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^4, {x, 0, nmax}], x] // Drop[#, 4] &
%Y A341481 Cf. A005171, A018252, A052284, A076608, A340960, A341451, A341462, A341480, A341482, A341483, A341484, A341485, A341486.
%K A341481 nonn
%O A341481 4,4
%A A341481 _Ilya Gutkovskiy_, Feb 13 2021