This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A253803 #10 Jan 10 2017 05:01:59 %S A253803 6,39,60,210,210,410,630,915,1320,1780,2340,990,2730,3164,4620,5215, %T A253803 5610,4290,8145,8106,2730,6630,12116,12540,4080,17485,17451,18480, %U A253803 9690,24414 %N A253803 a(n) gives one fourth of the even leg of one of the two Pythagorean triangles with hypotenuse A080109(n) = A002144(n)^2. The odd leg is given in A253802(n). %C A253803 See A253802 for comments and the Dickson reference. %D A253803 L. E. Dickson, History of the Theory of Numbers, Carnegie Institution, Publ. No. 256, Vol. II, Washington D.C., 1920, p. 227. %F A253803 a(n) = sqrt(A080109(n)^2 - A253802(n)^2)/4, n >= 1. %e A253803 n = 7: A080175(7) = 7890481 = 53^4 = 2809^2; A002144(7)^4 = A253802(7)^2 + (4*a(7))^2 = 1241^2 + (4*630)^2. %e A253803 The other Pythagorean triangle with hypotenuse %e A253803 53^2 = 2809 has odd leg A253804(7) = 2385 and even leg 4*A253305(7) = 4*371 = 1484: 53^4 = 2385^2 + (4*371)^2. %Y A253803 Cf. A002144, A080109, A253802, A253804, A253805. %K A253803 nonn,easy %O A253803 1,1 %A A253803 _Wolfdieter Lang_, Jan 14 2015