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A341468 Number of partitions of n into 9 distinct nonprime parts.

%I A341468 #10 Feb 28 2022 10:20:09
%S A341468 1,1,1,1,2,2,4,5,6,7,11,12,18,20,25,30,38,45,57,67,81,95,114,133,162,
%T A341468 187,219,255,297,343,401,462,529,607,696,793,910,1032,1168,1324,1497,
%U A341468 1689,1905,2142,2400,2692,3009,3362,3754,4182,4643,5165
%N A341468 Number of partitions of n into 9 distinct nonprime parts.
%p A341468 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341468       `if`(t=0, 1, 0), `if`(i<t or t<1, 0, b(n, i-1, t)+
%p A341468       `if`(isprime(i), 0, b(n-i, min(n-i, i-1), t-1))))
%p A341468     end:
%p A341468 a:= n-> b(n$2, 9):
%p A341468 seq(a(n), n=79..130);  # _Alois P. Heinz_, Feb 12 2021
%t A341468 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341468      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341468      If[PrimeQ[i], 0, b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t A341468 a[n_] := b[n, n, 9];
%t A341468 Table[a[n], {n, 79, 130}] (* _Jean-François Alcover_, Feb 28 2022, after _Alois P. Heinz_ *)
%Y A341468 Cf. A005171, A018252, A096258, A219203, A302479, A341457, A341461, A341462, A341464, A341465, A341466, A341467, A341469.
%K A341468 nonn
%O A341468 79,5
%A A341468 _Ilya Gutkovskiy_, Feb 12 2021