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 A384566 #7 Jun 14 2025 18:03:16
%S A384566 0,30,546,3900,17220,56730,153510,360696,762120,1482390,2698410,
%T A384566 4652340,7665996,12156690,18654510,27821040,40469520,57586446,
%U A384566 80354610,110177580,148705620,197863050,259877046,337307880,433080600,550518150,693375930,865877796,1072753500,1319277570,1611309630
%N A384566 Area of the unique primitive Pythagorean triple whose inradius is A002378(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%C A384566 a(n) is multiple of 6 for all n.
%H A384566 José Miguel Blanco Casado and Miguel Ángel Pérez García-Ortega, <a href="/A383833/a383833.pdf">El Libro de las Ternas Pitagóricas</a>
%F A384566 a(n) = (A384288(n,1) * A384288(n,2))/2.
%F A384566 a(n) = A002378(n)*(A002378(n) + 1)*(2*A002378(n) + 1).
%e A384566 For n=1, the short leg is A384288(1,1) = 5 and the long leg is A384288(1,2) = 12 so the area is then a(1) = (5 * 12 )/2 = 30.
%t A384566 a=Table[(n(n+1)),{n,0,30}];Apply[Join,Map[{#(#+1)(2#+1)}&,a]]
%Y A384566 Cf. A002378, A384288, A008514, A237516.
%K A384566 nonn,easy
%O A384566 0,2
%A A384566 _Miguel-Ángel Pérez García-Ortega_, Jun 03 2025