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 A065532 #40 Jan 16 2025 18:47:13
%S A065532 -1,47,191,431,767,1199,1727,2351,3071,3887,4799,5807,6911,8111,9407,
%T A065532 10799,12287,13871,15551,17327,19199,21167,23231,25391,27647,29999,
%U A065532 32447,34991,37631,40367,43199,46127,49151,52271,55487,58799,62207,65711,69311,73007,76799
%N A065532 a(n) = 48*n^2 - 1.
%H A065532 Harry J. Smith, <a href="/A065532/b065532.txt">Table of n, a(n) for n = 0..1000</a>
%H A065532 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A065532 From _Vincenzo Librandi_, Jul 08 2012: (Start)
%F A065532 G.f.: (1 - 50*x - 47*x^2)/(x-1)^3.
%F A065532 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A065532 From _Amiram Eldar_, Mar 19 2023: (Start)
%F A065532 Sum_{n>=1} 1/a(n) = (1 - cot(Pi/(4*sqrt(3)))*Pi/(4*sqrt(3)))/2.
%F A065532 Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/(4*sqrt(3)))*Pi/(4*sqrt(3)) - 1)/2. (End)
%F A065532 From _Elmo R. Oliveira_, Jan 16 2025: (Start)
%F A065532 E.g.f.: exp(x)*(48*x^2 + 48*x - 1).
%F A065532 a(n) = A158463(2*n). (End)
%t A065532 CoefficientList[Series[(1-50*x-47*x^2)/(x-1)^3,{x,0,40}],x] (* _Vincenzo Librandi_, Jul 08 2012 *)
%t A065532 LinearRecurrence[{3,-3,1},{-1,47,191},40] (* _Harvey P. Dale_, Dec 13 2017 *)
%o A065532 (PARI) A065532(n)=48*n^2-1
%o A065532 (Magma) [48*n^2 - 1: n in [0..50]]; // _Vincenzo Librandi_, Jul 08 2012
%Y A065532 Cf. A158463.
%K A065532 sign,easy
%O A065532 0,2
%A A065532 _Labos Elemer_, Nov 28 2001
%E A065532 Better description from _Randall L Rathbun_, Jan 19 2002
%E A065532 Offset changed from 1 to 0 by _Harry J. Smith_, Oct 21 2009