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 A158544 #32 Jan 16 2025 20:40:06
%S A158544 23,95,215,383,599,863,1175,1535,1943,2399,2903,3455,4055,4703,5399,
%T A158544 6143,6935,7775,8663,9599,10583,11615,12695,13823,14999,16223,17495,
%U A158544 18815,20183,21599,23063,24575,26135,27743,29399,31103,32855,34655,36503,38399,40343,42335
%N A158544 a(n) = 24*n^2 - 1.
%C A158544 The identity (24*n^2 - 1)^2 - (144*n^2 - 12)*(2*n)^2 = 1 can be written as a(n)^2 - A158543(n)*A005843(n)^2 = 1.
%H A158544 Vincenzo Librandi, <a href="/A158544/b158544.txt">Table of n, a(n) for n = 1..10000</a>
%H A158544 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A158544 From _Vincenzo Librandi_, Feb 14 2012: (Start)
%F A158544 G.f.: -x*(23 + 26*x - x^2)/(x - 1)^3.
%F A158544 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A158544 From _Amiram Eldar_, Mar 06 2023: (Start)
%F A158544 Sum_{n>=1} 1/a(n) = (1 - cot(Pi/(2*sqrt(6)))*Pi/(2*sqrt(6)))/2.
%F A158544 Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/(2*sqrt(6)))*Pi/(2*sqrt(6)) - 1)/2. (End)
%F A158544 From _Elmo R. Oliveira_, Jan 16 2025: (Start)
%F A158544 E.g.f.: exp(x)*(24*x^2 + 24*x - 1) + 1.
%F A158544 a(n) = A140811(2*n). (End)
%t A158544 LinearRecurrence[{3, -3, 1}, {23, 95, 215}, 50] (* _Vincenzo Librandi_, Feb 14 2012 *)
%o A158544 (Magma) I:=[23, 95, 215]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 14 2012
%o A158544 (PARI) for(n=1, 40, print1(24*n^2 - 1", ")); \\ _Vincenzo Librandi_, Feb 14 2012
%Y A158544 Cf. A005843, A140811, A158543.
%K A158544 nonn,easy
%O A158544 1,1
%A A158544 _Vincenzo Librandi_, Mar 21 2009
%E A158544 Comment rewritten by _R. J. Mathar_, Oct 16 2009