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A341466 Number of partitions of n into 7 distinct nonprime parts.

%I A341466 #11 Feb 23 2022 06:47:40
%S A341466 1,0,1,1,2,2,4,3,6,6,9,9,14,15,21,23,30,33,43,47,61,67,81,91,112,123,
%T A341466 150,165,194,217,255,281,330,363,417,461,529,582,665,730,823,905,1018,
%U A341466 1115,1253,1368,1519,1662,1844,2010,2227,2419,2659,2894,3175,3442
%N A341466 Number of partitions of n into 7 distinct nonprime parts.
%p A341466 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341466       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341466       `if`(isprime(i), 0, b(n-i, min(n-i, i-1), t-1))))
%p A341466     end:
%p A341466 a:= n-> b(n$2, 7):
%p A341466 seq(a(n), n=50..105);  # _Alois P. Heinz_, Feb 12 2021
%t A341466 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341466      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341466      If[PrimeQ[i], 0, b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t A341466 a[n_] := b[n, n, 7];
%t A341466 Table[a[n], {n, 50, 105}] (* _Jean-François Alcover_, Feb 23 2022, after _Alois P. Heinz_ *)
%Y A341466 Cf. A005171, A018252, A096258, A219201, A302479, A341454, A341461, A341462, A341464, A341465, A341467.
%K A341466 nonn
%O A341466 50,5
%A A341466 _Ilya Gutkovskiy_, Feb 12 2021