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%I #7 Feb 13 2021 14:18:30
%S 1,0,0,8,0,8,28,8,64,64,84,232,182,400,596,680,1232,1520,2128,3144,
%T 3970,5504,7532,9584,12945,16920,21464,28288,35778,45264,57856,72024,
%U 90036,112456,138140,170600,208874,254192,309088,373584,449731,539408,645584,767776
%N Number of ways to write n as an ordered sum of 8 nonprime numbers.
%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, 8):
%p seq(a(n), n=8..51); # _Alois P. Heinz_, Feb 13 2021
%t nmax = 51; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 8] &
%Y Cf. A005171, A018252, A052284, A076608, A340964, A341455, A341467, A341480, A341481, A341482, A341483, A341484, A341486.
%K nonn
%O 8,4
%A _Ilya Gutkovskiy_, Feb 13 2021
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