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A341983 Number of ways to write n as an ordered sum of 4 primes (counting 1 as a prime).

%I A341983 #8 Feb 25 2021 15:28:35
%S A341983 1,4,10,16,23,28,38,44,55,52,62,60,84,80,106,88,123,108,160,128,184,
%T A341983 136,214,168,261,172,270,168,304,204,352,200,382,232,442,264,470,232,
%U A341983 502,268,557,300,608,292,672,340,722,372,789,356,856,396,900,432,968,380,1024,432
%N A341983 Number of ways to write n as an ordered sum of 4 primes (counting 1 as a prime).
%H A341983 Alois P. Heinz, <a href="/A341983/b341983.txt">Table of n, a(n) for n = 4..10000</a>
%F A341983 G.f.: ( x + Sum_{k>=1} x^prime(k) )^4.
%p A341983 b:= proc(n) option remember; series(`if`(n=0, 1, x*add(
%p A341983       `if`(j=1 or isprime(j), b(n-j), 0), j=1..n)), x, 5)
%p A341983     end:
%p A341983 a:= n-> coeff(b(n), x, 4):
%p A341983 seq(a(n), n=4..61);  # _Alois P. Heinz_, Feb 24 2021
%t A341983 nmax = 61; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^4, {x, 0, nmax}], x] // Drop[#, 4] &
%Y A341983 Cf. A008578, A280917, A283762, A340960, A341947, A341975, A341982, A341984.
%K A341983 nonn
%O A341983 4,2
%A A341983 _Ilya Gutkovskiy_, Feb 24 2021