%I #26 Feb 01 2021 20:51:13
%S 0,0,8,12,24,32,48,108,152,96,120,456,168,192,784,684,288,608,360,
%T 1416,1624,480,528,3188,1224,672,2096,2856,840,3136,960,3756,4144,
%U 1152,4200,7908,1368,1440,5824,9336,1680,6496,1848,7176,12480,2112,2208,19300,4752,4896
%N Sum of the areas of all r X s rectangles such that r < s, r + s = 2n and (s - r) | (s * r).
%F a(n) = Sum_{i=1..n-1} i * (2*n-i) * chi(i*(2*n-i)/(2*n-2*i)), where chi(n) = 1 - ceiling(n) + floor(n).
%e a(8) = 108; 2*8 = 16 has two rectangles, 4 X 12 and 6 X 10, such that (12 - 4) | (12 * 4) = 8 | 48 and (10 - 6) | (10 * 6) = 4 | 60. The sum of the areas of the rectangles is 4*12 + 6*10 = 48 + 60 = 108.
%t Table[Sum[i (2 n - i) (1 - Ceiling[(i (2 n - i))/(2 n - 2 i)] + Floor[(i (2 n - i))/(2 n - 2 i)]), {i, n - 1}], {n, 80}]
%K nonn,easy
%O 1,3
%A _Wesley Ivan Hurt_, Apr 23 2020