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 A385187 #6 Jul 02 2025 16:42:00
%S A385187 1,6,330,3036,14820,51330,142926,341880,731016,1433790,2625810,
%T A385187 4547796,7519980,11957946,18389910,27475440,40025616,57024630,
%U A385187 79652826,109311180,147647220,196582386,258340830,335479656,430920600,547983150,690419106,862448580,1068797436,1314736170,1606120230
%N A385187 Area of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A002378(n) and its long leg and hypotenuse are consecutive natural numbers.
%C A385187 a(n) is a multiple of 6 for all n.
%H A385187 José-Miguel Blanco Casado and Miguel-Ángel Pérez García-Ortega, <a href="/A382844/a382844.pdf">El Libro de las Ternas Pitagóricas</a>
%F A385187 a(n) = (A385022(n,1) * A385022(n,2))/2.
%F A385187 a(n) = A002378(n)*(A002378(n) - 1)*(2*A002378(n) - 1).
%e A385187 For n=2, the short leg is A385022(2,1) = 11 and the long leg is A385022(2,2) = 60 so the area is then a(2) = (11 * 60)/2 = 330.
%t A385187 a=Table[n(n+1),{n,1,30}];Apply[Join,Map[{#(#-1)(2#-1)}&,a]]
%Y A385187 Cf. A002378, A385022, A142463.
%K A385187 nonn,easy
%O A385187 1,2
%A A385187 _Miguel-Ángel Pérez García-Ortega_, Jun 20 2025