

A308982


Areas of integer rectangles circumscribed by increasingly large circles.


0



1, 2, 4, 3, 6, 4, 9, 8, 12, 5, 10, 16, 15, 6, 12, 20, 18, 7, 25, 24, 14, 21, 30, 8, 28, 16, 36, 24, 35, 32, 9, 18, 42, 40, 27, 36, 49, 48, 10, 20, 45, 30, 56, 40, 54, 11, 22, 50, 64, 33, 63, 60, 44, 12, 72, 55, 24, 70, 36, 66, 48, 81, 80, 60, 13, 77, 26, 39
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OFFSET

1,2


COMMENTS

Sort all rectangles with integer side lengths by the radius of the circle that circumscribes them. Ties are broken by sorting by area. The terms of the sequence are the areas of the rectangles.


LINKS



EXAMPLE

a(1) is a 1 X 1 rectangle; r = sqrt(1^2 + 1^2) = sqrt(2); A = 1.
a(2) is a 2 X 1 rectangle; r = sqrt(2^2 + 1^2) = sqrt(5); A = 2.


MATHEMATICA

Times @@@ Take[Flatten[ SortBy[#, Times @@ # &] & /@ GatherBy[ SortBy[ Union[Sort /@ Tuples[ Range[70], 2]], Total[#^2] &], Total[#^2] &], 1], 70] (* Giovanni Resta, Jul 18 2019 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



