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A341455 Number of partitions of n into 8 nonprime parts.

%I A341455 #11 Feb 23 2022 06:49:19
%S A341455 1,0,0,1,0,1,1,1,2,2,2,3,3,4,6,6,7,9,10,12,15,17,20,24,28,32,38,43,51,
%T A341455 59,67,77,90,101,119,133,152,172,199,220,256,283,325,359,412,453,520,
%U A341455 569,652,711,810,882,1005,1091,1238,1341,1519,1641,1854,1999
%N A341455 Number of partitions of n into 8 nonprime parts.
%p A341455 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341455       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341455       `if`(isprime(i), 0, b(n-i, min(n-i, i), t-1))))
%p A341455     end:
%p A341455 a:= n-> b(n$2, 8):
%p A341455 seq(a(n), n=8..67);  # _Alois P. Heinz_, Feb 12 2021
%t A341455 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341455      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341455      If[PrimeQ[i], 0, b[n - i, Min[n - i, i], t - 1], 0]]];
%t A341455 a[n_] := b[n, n, 8];
%t A341455 Table[a[n], {n, 8, 67}] (* _Jean-François Alcover_, Feb 23 2022, after _Alois P. Heinz_ *)
%Y A341455 Cf. A002095, A005171, A018252, A062610, A259198, A341408, A341451, A341452, A341453, A341454, A341457.
%K A341455 nonn
%O A341455 8,9
%A A341455 _Ilya Gutkovskiy_, Feb 12 2021