%I #4 Apr 09 2021 09:40:11
%S 0,0,0,0,0,0,1,0,1,1,5,0,8,4,4,3,16,3,21,5,14,18,33,3,31,29,30,20,56,
%T 13,65,31,52,59,59,20,96,78,80,40,120,49,133,82,83,124,161,50,156,116,
%U 154,129,208,109,181,119,200,213,261,80,280,248,204,196,267,193,341,255
%N Number of partitions of n into 3 parts such that no part divides n.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - sign(c(i/j) + c((n-i-j)/j) + c((n-i-j)/i))), where c(n) = 1 - ceiling(n) + floor(n).
%e a(10) = 1; [4,3,3];
%e a(11) = 5; [7,2,2], [6,3,2], [5,4,2], [5,3,3], [4,4,3];
%e a(12) = 0; (Every partition of 12 into 3 parts contains at least one part that divides 12: [10,1,1], [9,2,1], [8,3,1], [7,4,1], [6,5,1], [8,2,2], [7,3,2], [6,4,2], [5,5,2], [6,3,3], [5,4,3], [4,4,4].);
%e a(13) = 8; [9,2,2], [8,3,2], [7,4,2], [6,5,2], [7,3,3], [6,4,3], [5,5,3], [5,4,4].
%Y Cf. A343126.
%K nonn
%O 1,11
%A _Wesley Ivan Hurt_, Apr 08 2021