

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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

Table of n, a(n) for n=1..68.


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

Cf. A024509.
Sequence in context: A151734 A175027 A269837 * A182298 A182732 A119477
Adjacent sequences: A308979 A308980 A308981 * A308983 A308984 A308985


KEYWORD

nonn


AUTHOR

Dave Rutt, Jul 04 2019


EXTENSIONS

More terms from Giovanni Resta, Jul 17 2019


STATUS

approved



