OFFSET
1,3
FORMULA
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).
EXAMPLE
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.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 23 2020
STATUS
approved