cp's OEIS Frontend

A341949 Number of partitions of n into 6 primes (counting 1 as a prime).

%I A341949 #11 Feb 15 2022 08:15:52
%S A341949 1,1,2,2,4,4,7,6,9,8,12,10,16,12,19,15,24,18,29,21,35,25,41,29,49,33,
%T A341949 56,37,63,41,72,46,82,51,91,58,105,63,115,68,128,77,143,83,158,90,174,
%U A341949 101,193,107,211,116,231,128,250,134,273,142,294,157,321,165,347,176,374
%N A341949 Number of partitions of n into 6 primes (counting 1 as a prime).
%p A341949 b:= proc(n, i) option remember; series(`if`(n=0, 1,
%p A341949      `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i)))(
%p A341949      `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 7)
%p A341949     end:
%p A341949 a:= n-> coeff(b(n, numtheory[pi](n)), x, 6):
%p A341949 seq(a(n), n=6..70);  # _Alois P. Heinz_, Feb 24 2021
%t A341949 b[n_, i_] := b[n, i] = Series[If[n == 0, 1,
%t A341949      If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i]]][
%t A341949      If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 7}];
%t A341949 a[n_] := Coefficient[b[n, PrimePi[n]], x, 6];
%t A341949 Table[a[n], {n, 6, 70}] (* _Jean-François Alcover_, Feb 15 2022, after _Alois P. Heinz_ *)
%Y A341949 Cf. A008578, A034891, A259196, A341945, A341946, A341947, A341948, A341950, A341951.
%K A341949 nonn
%O A341949 6,3
%A A341949 _Ilya Gutkovskiy_, Feb 24 2021