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 A158558 #30 Mar 09 2023 04:18:58
%S A158558 1,31,121,271,481,751,1081,1471,1921,2431,3001,3631,4321,5071,5881,
%T A158558 6751,7681,8671,9721,10831,12001,13231,14521,15871,17281,18751,20281,
%U A158558 21871,23521,25231,27001,28831,30721,32671,34681,36751,38881,41071,43321,45631,48001,50431
%N A158558 a(n) = 30*n^2 + 1.
%C A158558 The identity (30*n^2+1)^2 - (225*n^2+15)*(2*n)^2 = 1 can be written as a(n)^2 - A158557(n)*A005843(n)^2 = 1.
%H A158558 Vincenzo Librandi, <a href="/A158558/b158558.txt">Table of n, a(n) for n = 0..10000</a>
%H A158558 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A158558 G.f.: (1 + 28*x + 31*x^2)/(1 - x)^3.
%F A158558 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A158558 From _Amiram Eldar_, Mar 09 2023: (Start)
%F A158558 Sum_{n>=0} 1/a(n) = (coth(Pi/sqrt(30))*Pi/sqrt(30) + 1)/2.
%F A158558 Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(30))*Pi/sqrt(30) + 1)/2. (End)
%t A158558 LinearRecurrence[{3, -3, 1}, {1, 31, 121}, 50] (* _Vincenzo Librandi_, Feb 14 2012 *)
%t A158558 30*Range[0,40]^2+1 (* _Harvey P. Dale_, Mar 06 2013 *)
%o A158558 (Magma) I:=[1, 31, 121]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Feb 14 2012
%o A158558 (PARI) for(n=0, 40, print1(30*n^2 + 1", ")); \\ _Vincenzo Librandi_, Feb 14 2012
%Y A158558 Cf. A005843, A158557.
%K A158558 nonn,easy
%O A158558 0,2
%A A158558 _Vincenzo Librandi_, Mar 21 2009
%E A158558 Comment rewritten, and a(0) added by _R. J. Mathar_, Oct 16 2009