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 A162269 #21 Sep 08 2022 08:45:46
%S A162269 5,12,38,128,436,1488,5080,17344,59216,202176,690272,2356736,8046400,
%T A162269 27472128,93795712,320238592,1093362944,3732974592,12745172480,
%U A162269 43514740736,148568617984,507244990464,1731842725888,5912880922624
%N A162269 a(n) = ((5+sqrt(2))*(2+sqrt(2))^n + (5-sqrt(2))*(2-sqrt(2))^n)/2.
%C A162269 Second binomial transform of A162396.
%H A162269 G. C. Greubel, <a href="/A162269/b162269.txt">Table of n, a(n) for n = 0..1000</a>
%H A162269 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4, -2).
%F A162269 a(n) = 4*a(n-1) - 2*a(n-2) for n>1; a(0) = 5, a(1) = 12.
%F A162269 G.f.: (5-8*x)/(1-4*x+2*x^2).
%F A162269 From _G. C. Greubel_, Oct 02 2018: (Start)
%F A162269 a(2*n) = 2^(n-1)*(Q(2*n+1) + 4*Q(2*n)), where Q(m) = Pell-Lucas numbers.
%F A162269 a(2*n+1) = 2^(n+1)*(P(2*n+2) + 4*P(2*n+1)), where P(m) = Pell numbers. (End)
%F A162269 a(n) = 5*A007070(n)-8*A007070(n-1). - _R. J. Mathar_, Feb 04 2021
%t A162269 LinearRecurrence[{4,-2},{5,12},30] (* _Harvey P. Dale_, Jan 03 2016 *)
%o A162269 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+r)*(2+r)^n+(5-r)*(2-r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 02 2009
%o A162269 (PARI) x='x+O('x^30); Vec((5-8*x)/(1-4*x+2*x^2)) \\ _G. C. Greubel_, Oct 02 2018
%Y A162269 Cf. A162396.
%K A162269 nonn,easy
%O A162269 0,1
%A A162269 Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009
%E A162269 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 02 2009