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 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

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Last modified July 13 20:42 EDT 2024. Contains 374288 sequences. (Running on oeis4.)