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A341482 Number of ways to write n as an ordered sum of 5 nonprime numbers.

%I A341482 #7 Feb 13 2021 14:02:16
%S A341482 1,0,0,5,0,5,10,5,25,15,30,55,45,85,105,126,180,220,260,360,415,510,
%T A341482 650,745,915,1101,1270,1525,1800,2045,2440,2780,3225,3660,4250,4771,
%U A341482 5465,6185,6930,7840,8816,9790,11015,12240,13505,15146,16595,18385,20240,22325,24255
%N A341482 Number of ways to write n as an ordered sum of 5 nonprime numbers.
%p A341482 b:= proc(n, t) option remember;
%p A341482       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p A341482       `if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))
%p A341482     end:
%p A341482 a:= n-> b(n, 5):
%p A341482 seq(a(n), n=5..55);  # _Alois P. Heinz_, Feb 13 2021
%t A341482 nmax = 55; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^5, {x, 0, nmax}], x] // Drop[#, 5] &
%Y A341482 Cf. A005171, A018252, A052284, A076608, A340961, A341452, A341464, A341480, A341481, A341483, A341484, A341485, A341486.
%K A341482 nonn
%O A341482 5,4
%A A341482 _Ilya Gutkovskiy_, Feb 13 2021