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 A163609 #11 Sep 08 2022 08:45:46
%S A163609 5,19,79,341,1493,6571,28975,127853,564293,2490787,10994671,48532517,
%T A163609 214232405,945666811,4174374031,18426576509,81338840837,359047009459,
%U A163609 1584910170895,6996131959157,30882420558677,136321599637963
%N A163609 a(n) = ((5 + 2*sqrt(2))*(3 + sqrt(2))^n + (5 - 2*sqrt(2))*(3 - sqrt(2))^n)/2.
%C A163609 Binomial transform of A163608. Third binomial transform of A163888. Inverse binomial transform of A163610.
%H A163609 G. C. Greubel, <a href="/A163609/b163609.txt">Table of n, a(n) for n = 0..1000</a>
%H A163609 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-7).
%F A163609 a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 5, a(1) = 19.
%F A163609 G.f.: (5-11*x)/(1-6*x+7*x^2).
%F A163609 a(n) = 5*A081179(n+1) - 11*A081179(n). - _R. J. Mathar_, Nov 08 2013
%F A163609 E.g.f.: exp(3*x)*( 5*cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Jul 29 2017
%t A163609 LinearRecurrence[{6, -7}, {5, 19}, 50] (* _G. C. Greubel_, Jul 29 2017 *)
%o A163609 (Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+2*r)*(3+r)^n+(5-2*r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 06 2009
%o A163609 (PARI) x='x+O('x^50); Vec((5-11*x)/(1-6*x+7*x^2)) \\ _G. C. Greubel_, Jul 29 2017
%Y A163609 Cf. A163608, A163610, A163888.
%K A163609 nonn,easy
%O A163609 0,1
%A A163609 Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
%E A163609 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 06 2009