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 A025169 #73 Sep 08 2022 08:44:48
%S A025169 2,6,16,42,110,288,754,1974,5168,13530,35422,92736,242786,635622,
%T A025169 1664080,4356618,11405774,29860704,78176338,204668310,535828592,
%U A025169 1402817466,3672623806,9615053952,25172538050,65902560198,172535142544
%N A025169 a(n) = 2*Fibonacci(2*n+2).
%C A025169 The pairs (x, y) = (a(n), a(n+1)) satisfy x^2 + y^2 = 3*x*y + 4. - _Michel Lagneau_, Feb 01 2014
%H A025169 Vincenzo Librandi, <a href="/A025169/b025169.txt">Table of n, a(n) for n = 0..200</a>
%H A025169 Hacène Belbachir, Soumeya Merwa Tebtoub, László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Nemeth/nemeth7.html">Ellipse Chains and Associated Sequences</a>, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
%H A025169 Mark W. Coffey, James L. Hindmarsh, Matthew C. Lettington, John Pryce, <a href="http://arxiv.org/abs/1502.03085">On Higher Dimensional Interlacing Fibonacci Sequences, Continued Fractions and Chebyshev Polynomials</a>, arXiv:1502.03085 [math.NT], 2015 (see p. 32).
%H A025169 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A025169 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1).
%F A025169 G.f.: 2/(1 - 3*x + x^2).
%F A025169 a(n) = 3*a(n-1) - a(n-2).
%F A025169 a(n) = 2*A001906(n+1).
%F A025169 a(n) = A111282(n+2). - _Reinhard Zumkeller_, Apr 08 2012
%F A025169 a(n) = Fibonacci(2*n+1) + Lucas(2*n+1). - _Bruno Berselli_, Oct 13 2017
%p A025169 seq( 2*fibonacci(2*n+2), n=0..30); # _G. C. Greubel_, Jan 16 2020
%t A025169 Table[2Fibonacci[2n+2], {n,0,30}] (* or *)
%t A025169 CoefficientList[Series[2/(1-3x+x^2), {x,0,30}], x] (* _Michael De Vlieger_, Mar 09 2016 *)
%t A025169 LinearRecurrence[{3, -1}, {2, 6}, 30] (* _Jean-François Alcover_, Sep 27 2017 *)
%o A025169 (PARI) a(n)=2*fibonacci(2*n+2)
%o A025169 (Magma) [2*Fibonacci(2*n+2): n in [0..30]]; // _Vincenzo Librandi_, Jul 11 2011
%o A025169 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 2/(1-3*x + x^2) )); // _Marius A. Burtea_, Jan 16 2020
%o A025169 (Haskell)
%o A025169 a025169 n = a025169_list !! n
%o A025169 a025169_list = 2 : 6 : zipWith (-) (map (* 3) $ tail a025169_list) a025169_list
%o A025169 -- _Reinhard Zumkeller_, Apr 08 2012
%o A025169 (Sage) [2*fibonacci(2*n+2) for n in (0..30)] # _G. C. Greubel_, Jan 16 2020
%o A025169 (GAP) List([0..30], n-> 2*Fibonacci(2*n+2) ); # _G. C. Greubel_, Jan 16 2020
%Y A025169 Cf. A000032, A000045, A001906, A002878, A122367.
%K A025169 nonn,easy
%O A025169 0,1
%A A025169 _Wouter Meeussen_
%E A025169 Better description from _Michael Somos_