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 A162268 #20 Mar 15 2024 02:23:20
%S A162268 5,7,19,45,109,263,635,1533,3701,8935,21571,52077,125725,303527,
%T A162268 732779,1769085,4270949,10310983,24892915,60096813,145086541,
%U A162268 350269895,845626331,2041522557,4928671445,11898865447,28726402339,69351670125
%N A162268 a(n) = ((5+sqrt(2))*(1+sqrt(2))^n + (5-sqrt(2))*(1-sqrt(2))^n)/2.
%C A162268 Binomial transform of A162396.
%H A162268 Vincenzo Librandi, <a href="/A162268/b162268.txt">Table of n, a(n) for n = 0..1000</a>
%H A162268 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,1)
%F A162268 a(n) = 2*a(n-1) + a(n-2) for n > 1; a(0) = 5, a(1) = 7.
%F A162268 G.f.: (5-3*x)/(1-2*x-x^2).
%F A162268 a(n) = 5*A000129(n+1) - 3*A000129(n). - _R. J. Mathar_, Mar 06 2013
%F A162268 a(n) = 4*A001333(n) + A001333(n+1). - _G. C. Greubel_, Aug 17 2018
%t A162268 LinearRecurrence[{2,1}, {5,7}, 30] (* _Vincenzo Librandi_, Feb 03 2018 *)
%t A162268 Table[(4*LucasL[n, 2] + LucasL[n + 1, 2])/2, {n, 0, 30}] (* _G. C. Greubel_, Aug 17 2018 *)
%o A162268 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+r)*(1+r)^n+(5-r)*(1-r)^n)/2: n in [0..27] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 02 2009
%o A162268 (PARI) x='x+O('x^30); Vec((5-3*x)/(1-2*x-x^2)) \\ _G. C. Greubel_, Aug 17 2018
%Y A162268 Cf. A162396.
%K A162268 nonn,easy
%O A162268 0,1
%A A162268 Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009
%E A162268 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 02 2009