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A341948 Number of partitions of n into 5 primes (counting 1 as a prime).

%I A341948 #12 Feb 15 2022 07:46:45
%S A341948 1,1,2,2,4,4,6,5,8,6,10,7,12,9,15,10,18,12,21,14,25,15,29,18,33,21,37,
%T A341948 20,41,23,46,26,51,27,58,31,63,34,68,33,77,39,83,42,90,43,101,48,107,
%U A341948 53,116,52,128,58,134,61,142,61,157,68,165,73,176,73,194,82,201,84,211
%N A341948 Number of partitions of n into 5 primes (counting 1 as a prime).
%H A341948 Alois P. Heinz, <a href="/A341948/b341948.txt">Table of n, a(n) for n = 5..10000</a>
%p A341948 b:= proc(n, i) option remember; series(`if`(n=0, 1,
%p A341948      `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i)))(
%p A341948      `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 6)
%p A341948     end:
%p A341948 a:= n-> coeff(b(n, numtheory[pi](n)), x, 5):
%p A341948 seq(a(n), n=5..73);  # _Alois P. Heinz_, Feb 24 2021
%t A341948 b[n_, i_] := b[n, i] = Series[If[n == 0, 1,
%t A341948      If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i]]][
%t A341948      If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 6}];
%t A341948 a[n_] := Coefficient[b[n, PrimePi[n]], x, 5];
%t A341948 Table[a[n], {n, 5, 73}] (* _Jean-François Alcover_, Feb 15 2022, after _Alois P. Heinz_ *)
%Y A341948 Cf. A008578, A034891, A259195, A341945, A341946, A341947, A341949, A341950, A341951.
%K A341948 nonn
%O A341948 5,3
%A A341948 _Ilya Gutkovskiy_, Feb 24 2021