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A341469 Number of partitions of n into 10 distinct nonprime parts.

%I A341469 #8 Feb 28 2022 10:46:10
%S A341469 1,0,1,1,2,2,4,3,6,7,10,11,17,17,25,28,38,44,57,64,82,95,117,136,168,
%T A341469 189,231,264,317,366,433,490,579,660,770,877,1019,1146,1327,1497,1720,
%U A341469 1940,2215,2481,2825,3165,3583,4008,4523,5033,5664
%N A341469 Number of partitions of n into 10 distinct nonprime parts.
%p A341469 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341469       `if`(t=0, 1, 0), `if`(i<t or t<1, 0, b(n, i-1, t)+
%p A341469       `if`(isprime(i), 0, b(n-i, min(n-i, i-1), t-1))))
%p A341469     end:
%p A341469 a:= n-> b(n$2, 10):
%p A341469 seq(a(n), n=95..145);  # _Alois P. Heinz_, Feb 12 2021
%t A341469 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341469      If[t == 0, 1, 0], If[i < t || t < 1, 0, b[n, i - 1, t] +
%t A341469      If[PrimeQ[i], 0, b[n - i, Min[n - i, i - 1], t - 1]]]];
%t A341469 a[n_] := b[n, n, 10];
%t A341469 Table[a[n], {n, 95, 145}] (* _Jean-François Alcover_, Feb 28 2022, after _Alois P. Heinz_ *)
%Y A341469 Cf. A005171, A018252, A096258, A219204, A302479, A341460, A341461, A341462, A341464, A341465, A341466, A341467, A341468.
%K A341469 nonn
%O A341469 95,5
%A A341469 _Ilya Gutkovskiy_, Feb 12 2021