A333754 Sum of the areas of all r X s rectangles such that r < s, r + s = 2n and (s - r) | (s * r).

0, 0, 8, 12, 24, 32, 48, 108, 152, 96, 120, 456, 168, 192, 784, 684, 288, 608, 360, 1416, 1624, 480, 528, 3188, 1224, 672, 2096, 2856, 840, 3136, 960, 3756, 4144, 1152, 4200, 7908, 1368, 1440, 5824, 9336, 1680, 6496, 1848, 7176, 12480, 2112, 2208, 19300, 4752, 4896

Offset

1,3

Links

Table of n, a(n) for n=1..50.

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

Sequence in context: A367146 A278902 A336583 * A088525 A054735 A162691

Adjacent sequences: A333751 A333752 A333753 * A333755 A333756 A333757

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 23 2020

Status

approved