Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #5 Apr 09 2021 09:40:05
%S 0,0,1,1,2,3,3,5,6,7,5,12,6,12,15,18,8,24,9,28,23,22,11,45,21,27,31,
%T 45,14,62,15,54,39,37,43,88,18,42,47,93,20,98,21,79,86,52,23,142,44,
%U 92,63,96,26,134,71,142,71,67,29,220,30,72,127,145,85,170,33,130,87,185
%N Number of partitions of n into 3 parts where at least 1 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)} sign(c(n/j) + c(n/i) + c(n/(n-i-j))), where c(n) = 1 - ceiling(n) + floor(n).
%e a(6) = 3; [1,1,4], [1,2,3], [2,2,2];
%e a(7) = 3; [5,1,1], [4,2,1], [3,3,1];
%e a(8) = 5; [6,1,1], [5,2,1], [4,3,1], [3,2,2], [3,3,2];
%e a(12) = 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].
%Y Cf. A343126.
%K nonn
%O 1,5
%A _Wesley Ivan Hurt_, Apr 08 2021