A294457 Sum of all the diagonals of the distinct rectangles that can be made with positive integer sides such that L + W = n, W < L. The sums are then rounded to the nearest integer.

0, 0, 4, 6, 15, 19, 33, 38, 57, 64, 87, 97, 124, 135, 168, 181, 218, 232, 274, 291, 337, 355, 407, 427, 482, 504, 565, 589, 654, 679, 749, 777, 851, 880, 959, 991, 1074, 1107, 1196, 1230, 1323, 1360, 1458, 1496, 1599, 1639, 1746, 1788, 1900, 1944, 2060, 2106

Offset: 1

Author

Wesley Ivan Hurt, Oct 30 2017

Keywords

• nonn
• easy

Examples

			a(4) = 6; There is only one 1 X 3 rectangle (there is no 2 X 2 rectangle since W < L) and sqrt(1^2 + 3^2) = sqrt(10). Since there are two diagonals in a rectangle, the total length is 2*sqrt(10). Then we have round(2*sqrt(10)) = round(6.32455532..) = 6.
		

Crossrefs

Cf. A050187.

Programs

Mathematica

Table[Round[2*Sum[Sqrt[i^2 + (n - i)^2], {i, Floor[(n-1)/2]}]], {n, 80}]

Formula

a(n) = round(2 * Sum_{i=1..floor((n-1)/2)} sqrt(i^2 + (n-i)^2)).