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A341451 Number of partitions of n into 4 nonprime parts.

%I A341451 #11 Aug 19 2021 05:12:23
%S A341451 1,0,0,1,0,1,1,1,2,2,2,3,3,4,6,5,7,8,9,10,13,13,17,17,22,21,27,27,34,
%T A341451 34,41,40,51,49,62,59,71,70,86,82,101,97,117,112,135,131,155,150,180,
%U A341451 170,202,196,228,222,259,248,291,281,324,314,361,348,404,388,445,431
%N A341451 Number of partitions of n into 4 nonprime parts.
%p A341451 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341451       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341451       `if`(isprime(i), 0, b(n-i, min(n-i, i), t-1))))
%p A341451     end:
%p A341451 a:= n-> b(n$2, 4):
%p A341451 seq(a(n), n=4..69);  # _Alois P. Heinz_, Feb 12 2021
%t A341451 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341451      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341451      If[PrimeQ[i], 0, b[n - i, Min[n - i, i], t - 1]]]];
%t A341451 a[n_] := b[n, n, 4];
%t A341451 Table[a[n], {n, 4, 69}] (* _Jean-François Alcover_, Aug 19 2021, after _Alois P. Heinz_ *)
%Y A341451 Cf. A002095, A005171, A018252, A062610, A259194, A341408, A341452, A341453, A341454, A341455, A341457.
%K A341451 nonn
%O A341451 4,9
%A A341451 _Ilya Gutkovskiy_, Feb 12 2021