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 A334808 #10 Jun 19 2022 23:23:41 %S A334808 50,200,338,450,578,800,1250,2602,1682,1800,2312,5188,6404,3200,4050, %T A334808 5000,15610,5618,13492,6728,15650,8450,8450,8450,9248,32002,10658, %U A334808 36866,14450,12800,14450,14450,14450,15842,31700,16200,20402,20000,18050,18818,87978,69164 %N A334808 Consider all the Pythagorean triangles with perimeter A010814(n). Then a(n) is the sum of the areas of the squares on all of their sides. %H A334808 Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a> %H A334808 Wikipedia, <a href="http://en.wikipedia.org/wiki/Pythagorean_triple">Pythagorean Triple</a>. %H A334808 <a href="/index/Ps#PyTrip">Index entries related to Pythagorean Triples</a>. %F A334808 a(n) = 2 * Sum_{k=1..floor(c(n)/3)} Sum_{i=k..floor((c(n)-k)/2)} sign(floor((i+k)/(c(n)-i-k+1))) * [i^2 + k^2 = (c(n)-i-k)^2] * (c(n)-i-k)^2, where c = A010814. - _Wesley Ivan Hurt_, May 13 2020 %e A334808 a(1) = 50; there is one Pythagorean triangle with perimeter A010814(1) = 12, [3,4,5]. The sum of the areas of the squares on its sides is 3^2 + 4^2 + 5^2 = 9 + 16 + 25 = 50. %e A334808 a(2) = 200; there is one Pythagorean triangle with perimeter A010814(2) = 24, [6,8,10]. The sum of the areas of the squares on its sides is 6^2 + 8^2 + 10^2 = 36 + 64 + 100 = 200. %Y A334808 Cf. A010814. %K A334808 nonn %O A334808 1,1 %A A334808 _Wesley Ivan Hurt_, May 12 2020