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%I #11 Jan 10 2017 05:02:10
%S 5,30,34,145,111,180,371,330,876,1560,1746,505,1635,840,3014,3570,
%T 5181,2249,1710,7980,1379,3435,10920,7230,2056,8970,14490,11240,4981,
%U 3900
%N a(n) gives one fourth of the even leg of the second of the two Pythagorean triangles with hypotenuse A080109(n) = A002144(n)^2. The odd leg is given in A253804.
%C See A253804 for comments and the Dickson reference.
%D L. E. Dickson, History of the Theory of Numbers, Carnegie Institution, Publ. No. 256, Vol. II, Washington D.C., 1920, p. 227.
%F a(n) = sqrt(A080109(n)^2 - A253804(n)^2)/4, n >= 1.
%e n = 7: A080175(7) = 7890481 = 53^4 = 2809^2; A002144(7)^4 = A253804(7)^2 + (4*a(7))^2 = 2385^2 + (4*371)^2.
%e The other Pythagorean triangle with hypotenuse 53^2 = 2809 has odd leg A253802(7) = 1241 and even leg 4*A253303(7) = 4*630 = 2520: 53^4 = 1241^2 + (4*630)^2.
%Y Cf. A002144, A080109, A253804, A253802, A253803.
%K nonn,easy
%O 1,1
%A _Wolfdieter Lang_, Jan 16 2015