

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.


1



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
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..52.


FORMULA

a(n) = round(2 * Sum_{i=1..floor((n1)/2)} sqrt(i^2 + (ni)^2)).


EXAMPLE

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.


MATHEMATICA

Table[Round[2*Sum[Sqrt[i^2 + (n  i)^2], {i, Floor[(n1)/2]}]], {n, 80}]


CROSSREFS

Cf. A050187.
Sequence in context: A117883 A106387 A034771 * A266883 A034764 A119034
Adjacent sequences: A294454 A294455 A294456 * A294458 A294459 A294460


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Oct 30 2017


STATUS

approved



