A341469 - OEIS

%I #8 Feb 28 2022 10:46:10

%S 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 189,231,264,317,366,433,490,579,660,770,877,1019,1146,1327,1497,1720,

%U 1940,2215,2481,2825,3165,3583,4008,4523,5033,5664

%N Number of partitions of n into 10 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, 10):

%p seq(a(n), n=95..145);  # _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 < t || t < 1, 0, b[n, i - 1, t] +

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

%t a[n_] := b[n, n, 10];

%t Table[a[n], {n, 95, 145}] (* _Jean-François Alcover_, Feb 28 2022, after _Alois P. Heinz_ *)

%Y Cf. A005171, A018252, A096258, A219204, A302479, A341460, A341461, A341462, A341464, A341465, A341466, A341467, A341468.

%K nonn

%O 95,5

%A _Ilya Gutkovskiy_, Feb 12 2021