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A341454 Number of partitions of n into 7 nonprime parts.

%I A341454 #11 Feb 23 2022 06:49:29
%S A341454 1,0,0,1,0,1,1,1,2,2,2,3,3,4,6,6,7,9,10,12,15,17,20,24,27,32,37,43,49,
%T A341454 58,64,76,85,99,111,129,140,166,182,210,230,267,290,336,362,418,451,
%U A341454 519,559,640,685,784,837,956,1020,1158,1232,1397,1483,1677,1776
%N A341454 Number of partitions of n into 7 nonprime parts.
%p A341454 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341454       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341454       `if`(isprime(i), 0, b(n-i, min(n-i, i), t-1))))
%p A341454     end:
%p A341454 a:= n-> b(n$2, 7):
%p A341454 seq(a(n), n=7..67);  # _Alois P. Heinz_, Feb 12 2021
%t A341454 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341454      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341454      If[PrimeQ[i], 0, b[n - i, Min[n - i, i], t - 1], 0]]];
%t A341454 a[n_] := b[n, n, 7];
%t A341454 Table[a[n], {n, 7, 67}] (* _Jean-François Alcover_, Feb 23 2022, after _Alois P. Heinz_ *)
%Y A341454 Cf. A002095, A005171, A018252, A062610, A259197, A341408, A341451, A341452, A341453, A341455, A341457.
%K A341454 nonn
%O A341454 7,9
%A A341454 _Ilya Gutkovskiy_, Feb 12 2021