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 A381721 #16 Jun 16 2025 09:44:12
%S A381721 17,7,31,49,127,287,721,1799,4607,11857,30751,79999,208657,544967,
%T A381721 1424671,3726449,9750527,25518367,66793681,174844999,457712767,
%U A381721 1198247057,3136953631,8212492799,21500328977,56288177287,147363690271,385802064049,1010041159807,2644319243807,6922913058001,18124414244999,47450320478207
%N A381721 Sum of the legs of the unique primitive Pythagorean triple whose inradius is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%D A381721 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A381721 Miguel-Ángel Pérez García-Ortega, <a href="/A381721/a381721.pdf">El Libro de las Ternas Pitagóricas</a>
%H A381721 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-6,4,2,-1).
%F A381721 a(n) = A380821(n,1) + A380821(n,2).
%F A381721 a(n) = 2*(Lucas(n))^2 + 4*Lucas(n) + 1.
%F A381721 G.f.: (x^5-33*x^4+41*x^3+37*x^2-61*x+17)/((x-1)*(x+1)*(x^2-3*x+1)*(x^2+x-1)). - _Alois P. Heinz_, Jun 16 2025
%e A381721 For n=2, the short leg is A380821(2,1) = 7 and the long leg is A380821(2,2) = 24 so the semiperimeter is then a(2) = 7 + 24 = 31.
%t A381721 a=Table[LucasL[n],{n,0,35}];Apply[Join,Map[{2#^2+4#+1}&,a]]
%Y A381721 Cf. A380821, A380823, A380824, A000032.
%K A381721 nonn,easy
%O A381721 0,1
%A A381721 _Miguel-Ángel Pérez García-Ortega_, Mar 05 2025
%E A381721 a(19) corrected by _Georg Fischer_, Jun 16 2025