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Number of partitions of n into 6 distinct nonprime parts.
9

%I #12 Feb 23 2022 06:47:59

%S 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 114,128,146,167,187,209,237,262,294,331,366,405,449,496,547,608,663,

%U 730,798,875,953,1050,1136,1239,1342,1463,1577,1723,1849,2008,2159,2334

%N Number of partitions of n into 6 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, 6):

%p seq(a(n), n=38..95); # _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, 6];

%t Table[a[n], {n, 38, 95}] (* _Jean-François Alcover_, Feb 23 2022, after _Alois P. Heinz_ *)

%Y Cf. A005171, A018252, A096258, A219200, A302479, A341453, A341461, A341462, A341464, A341466, A341467.

%K nonn

%O 38,5

%A _Ilya Gutkovskiy_, Feb 12 2021