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 A158065 #46 Sep 08 2022 08:45:42
%S A158065 37,73,109,145,181,217,253,289,325,361,397,433,469,505,541,577,613,
%T A158065 649,685,721,757,793,829,865,901,937,973,1009,1045,1081,1117,1153,
%U A158065 1189,1225,1261,1297,1333,1369,1405,1441,1477,1513,1549,1585,1621
%N A158065 a(n) = 36*n + 1.
%C A158065 The identity (36*n + 1)^2 - (36*n^2 + 2*n)*6^2 = 1 can be written as a(n)^2 - A158064(n)*6^2 = 1. - _Vincenzo Librandi_, Feb 11 2012
%C A158065 Parametrize Pythagorean triangles with parameters a and b and side lengths x = b^2 - a^2, y = 2*a*b and z = a^2 + b^2. Generate one Pythagorean triangle with a=n-1 and b=n and side lengths (x1, y1, z1), and another one with a=n, b=n+1 and side lengths (x2, y2, z2). Then 2*a(n) = x2 - x1 + 12*(y2-y1) + 6*(z2-z1). - _J. M. Bergot_, Jul 16 2013
%H A158065 Vincenzo Librandi, <a href="/A158065/b158065.txt">Table of n, a(n) for n = 1..10000</a>
%H A158065 E. J. Barbeau, <a href="http://www.math.toronto.edu/barbeau/home.html">Polynomial Excursions</a>, Chapter 10: <a href="http://www.math.toronto.edu/barbeau/hxpol10.pdf">Diophantine equations</a> (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(6^2*t+2)).
%H A158065 John Elias, <a href="/A158065/a158065.png">Illustration of Initial Terms: Hexagram of Triangular Perimeters</a>
%H A158065 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).
%F A158065 G.f.: x*(37-x)/(1-x)^2. - _Vincenzo Librandi_, Feb 11 2012
%F A158065 a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Feb 11 2012
%F A158065 a(n) = 12*A008585(n) + 1 (see illustration in links). - _John Elias_, Jun 29 2021
%t A158065 Range[37, 2000, 36] (* _Vladimir Joseph Stephan Orlovsky_, Jun 15 2011 *)
%t A158065 LinearRecurrence[{2, -1}, {37, 73}, 50] (* _Vincenzo Librandi_, Feb 11 2012 *)
%o A158065 (Magma) I:=[37, 73]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 11 2012
%o A158065 (PARI) for(n=1, 40, print1(36*n + 1", ")); \\ _Vincenzo Librandi_, Feb 11 2012
%Y A158065 Cf. A008585, A158064.
%K A158065 nonn,easy
%O A158065 1,1
%A A158065 _Vincenzo Librandi_, Mar 12 2009