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 A163069 #10 Sep 08 2022 08:45:46
%S A163069 4,9,34,104,344,1104,3584,11584,37504,121344,392704,1270784,4112384,
%T A163069 13307904,43065344,139362304,450985984,1459421184,4722786304,
%U A163069 15283257344,49457659904,160048349184,517927337984,1676048072704
%N A163069 a(n) = ((4+sqrt(5))*(1+sqrt(5))^n + (4-sqrt(5))*(1-sqrt(5))^n)/2.
%C A163069 Binomial transform A163141. Inverse binomial transform A163070.
%H A163069 G. C. Greubel, <a href="/A163069/b163069.txt">Table of n, a(n) for n = 0..1000</a>
%H A163069 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,4).
%F A163069 a(n) = 2*a(n-1) + 4*a(n-2) for n > 1; a(0) = 4, a(1) = 9.
%F A163069 G.f.: (4+x)/(1-2*x-4*x^2).
%F A163069 a(n) = 2^(n+1) * A000032(n) + 5 * 2^(n-1) * A000045(n). - _Diego Rattaggi_, Jun 27 2020
%t A163069 LinearRecurrence[{2, 4}, {4, 9}, 30] (* _G. C. Greubel_, Jan 08 2018 *)
%o A163069 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((4+r)*(1+r)^n+(4-r)*(1-r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 21 2009
%o A163069 (PARI) x='x+O('x^30); Vec((4+x)/(1-2*x-4*x^2)) \\ _G. C. Greubel_, Jan 08 2018
%Y A163069 Cf. A163141, A163070.
%K A163069 nonn
%O A163069 0,1
%A A163069 Al Hakanson (hawkuu(AT)gmail.com), Jul 20 2009
%E A163069 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 21 2009