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A341465 Number of partitions of n into 6 distinct nonprime parts.

%I A341465 #12 Feb 23 2022 06:47:59
%S A341465 1,0,1,1,2,2,4,3,6,5,8,10,13,13,18,20,26,30,36,40,49,55,65,76,88,97,
%T A341465 114,128,146,167,187,209,237,262,294,331,366,405,449,496,547,608,663,
%U A341465 730,798,875,953,1050,1136,1239,1342,1463,1577,1723,1849,2008,2159,2334
%N A341465 Number of partitions of n into 6 distinct nonprime parts.
%p A341465 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341465       `if`(t=0, 1, 0), `if`(i<t or t<1, 0, b(n, i-1, t)+
%p A341465       `if`(isprime(i), 0, b(n-i, min(n-i, i-1), t-1))))
%p A341465     end:
%p A341465 a:= n-> b(n$2, 6):
%p A341465 seq(a(n), n=38..95);  # _Alois P. Heinz_, Feb 12 2021
%t A341465 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341465      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341465      If[PrimeQ[i], 0, b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t A341465 a[n_] := b[n, n, 6];
%t A341465 Table[a[n], {n, 38, 95}] (* _Jean-François Alcover_, Feb 23 2022, after _Alois P. Heinz_ *)
%Y A341465 Cf. A005171, A018252, A096258, A219200, A302479, A341453, A341461, A341462, A341464, A341466, A341467.
%K A341465 nonn
%O A341465 38,5
%A A341465 _Ilya Gutkovskiy_, Feb 12 2021