A341468 - OEIS

%I #10 Feb 28 2022 10:20:09

%S 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 187,219,255,297,343,401,462,529,607,696,793,910,1032,1168,1324,1497,

%U 1689,1905,2142,2400,2692,3009,3362,3754,4182,4643,5165

%N Number of partitions of n into 9 distinct nonprime parts.

%p b:= proc(n, i, t) option remember; `if`(n=0,

%p       `if`(t=0, 1, 0), `if`(i<t or t<1, 0, b(n, i-1, t)+

%p       `if`(isprime(i), 0, b(n-i, min(n-i, i-1), t-1))))

%p     end:

%p a:= n-> b(n$2, 9):

%p seq(a(n), n=79..130);  # _Alois P. Heinz_, Feb 12 2021

%t b[n_, i_, t_] := b[n, i, t] = If[n == 0,

%t      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +

%t      If[PrimeQ[i], 0, b[n - i, Min[n - i, i - 1], t - 1], 0]]];

%t a[n_] := b[n, n, 9];

%t Table[a[n], {n, 79, 130}] (* _Jean-François Alcover_, Feb 28 2022, after _Alois P. Heinz_ *)

%Y Cf. A005171, A018252, A096258, A219203, A302479, A341457, A341461, A341462, A341464, A341465, A341466, A341467, A341469.

%K nonn

%O 79,5

%A _Ilya Gutkovskiy_, Feb 12 2021