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 A114569 #17 May 09 2025 07:58:42
%S A114569 8,35,143,575,2303,9215,36863,147455,589823,2359295,9437183,37748735,
%T A114569 150994943,603979775,2415919103,9663676415,38654705663,154618822655,
%U A114569 618475290623,2473901162495,9895604649983,39582418599935,158329674399743,633318697598975,2533274790395903
%N A114569 a(n) = 9*4^n - 1.
%C A114569 Squares of the cotangents of the arcsins of 1/(3*2^n).
%H A114569 Vincenzo Librandi, <a href="/A114569/b114569.txt">Table of n, a(n) for n = 0..1000</a>
%H A114569 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%F A114569 From _Philippe Deléham_, Nov 26 2008: (Start)
%F A114569 a(n) = 4*a(n-1) + 3, n>0; a(0)=8.
%F A114569 a(n) = 5*a(n-1) - 4*a(n-2), n>1; a(0)=8, a(1)=35.
%F A114569 G.f.: (8-5*x)/(1-5*x+4*x^2). (End)
%F A114569 From _Elmo R. Oliveira_, May 08 2025: (Start)
%F A114569 E.g.f.: exp(x)*(9*exp(3*x) - 1).
%F A114569 a(n) = A199208(n) - 2. (End)
%e A114569 a(2) = 143.
%t A114569 Table[(9*4^n) - 1, {n, 0, 23}] (* _Stefan Steinerberger_, Feb 16 2006 *)
%o A114569 (Magma) [9*4^n-1: n in [0..30]]; // _Vincenzo Librandi_, Oct 29 2011
%Y A114569 Cf. A024036, A097743, A156760, A199208.
%K A114569 easy,nonn
%O A114569 0,1
%A A114569 Al Hakanson (hawkuu(AT)excite.com), Feb 16 2006
%E A114569 More terms from _Stefan Steinerberger_, Feb 16 2006