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 A164033 #10 Sep 08 2022 08:45:47
%S A164033 2,9,40,177,782,3453,15244,67293,297050,1311249,5788144,25550121,
%T A164033 112783718,497851461,2197622740,9700776213,42821298098,189022355097,
%U A164033 834385043896,3683153777697,16258227358910,71767287709581
%N A164033 a(n) = ((4+3*sqrt(2))*(3+sqrt(2))^n + (4-3*sqrt(2))*(3-sqrt(2))^n)/4.
%C A164033 Binomial transform of A020727. Third binomial transform of A164090. Inverse binomial transform of A164034.
%H A164033 Matthew House, <a href="/A164033/b164033.txt">Table of n, a(n) for n = 0..1542</a>
%H A164033 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-7).
%F A164033 a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 2, a(1) = 9.
%F A164033 G.f.: (2-3*x)/(1-6*x+7*x^2).
%F A164033 E.g.f.: (2*cosh(sqrt(2)*x) + (3/sqrt(2))*sinh(sqrt(2)*x))*exp(3*x). - _G. C. Greubel_, Sep 08 2017
%t A164033 CoefficientList[Series[(2-3*x)/(1-6*x+7*x^2), {x, 0, 1000}],
%t A164033 x] (* or *) LinearRecurrence[{6,-7},{2,9}, 50] (* _G. C. Greubel_, Sep 08 2017 *)
%o A164033 (Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+3*r)*(3+r)^n+(4-3*r)*(3-r)^n)/4: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 09 2009
%o A164033 (PARI) x='x+O('x^50); Vec((2-3*x)/(1-6*x+7*x^2)) \\ _G. C. Greubel_, Sep 08 2017
%Y A164033 Cf. A020727, A164090 (2, 3, 4, 6, 8, 12), A164034.
%K A164033 nonn
%O A164033 0,1
%A A164033 Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009
%E A164033 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 09 2009