A341452 - OEIS

%I #11 Aug 19 2021 05:10:28

%S 1,0,0,1,0,1,1,1,2,2,2,3,3,4,6,6,7,9,9,12,14,16,18,22,24,29,31,38,40,

%T 49,50,62,65,77,81,97,98,120,122,144,149,176,178,212,214,251,255,299,

%U 304,352,355,412,417,482,485,559,564,643,650,742,745,850,856,965

%N Number of partitions of n into 5 nonprime parts.

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

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

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

%p     end:

%p a:= n-> b(n$2, 5):

%p seq(a(n), n=5..68);  # _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], t - 1]]]];

%t a[n_] := b[n, n, 5];

%t Table[a[n], {n, 5, 68}] (* _Jean-François Alcover_, Aug 19 2021, after _Alois P. Heinz_ *)

%Y Cf. A002095, A005171, A018252, A062610, A259195, A341408, A341451, A341453, A341454, A341455, A341457.

%K nonn

%O 5,9

%A _Ilya Gutkovskiy_, Feb 12 2021