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 A164589 #28 Sep 08 2022 08:45:47
%S A164589 1,4,15,58,221,848,3243,12422,47545,182044,696903,2668114,10214549,
%T A164589 39105896,149713635,573168542,2194332529,8400844852,32162017407,
%U A164589 123129948778,471394019405,1804697680256,6909153496347,26451190754486,101266455983401,387691247248204
%N A164589 a(n) = ((4 + 3*sqrt(2))*(1 + 2*sqrt(2))^n + (4 - 3*sqrt(2))*(1 - 2*sqrt(2))^n)/8.
%C A164589 Binomial transform of A096886. Inverse binomial transform of A086347.
%H A164589 G. C. Greubel, <a href="/A164589/b164589.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..100 from Vincenzo Librandi)
%H A164589 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,7).
%F A164589 a(n) = 2*a(n-1) + 7*a(n-2) for n > 1; a(0) = 1, a(1) = 4.
%F A164589 G.f.: (1 + 2*x)/(1 - 2*x - 7*x^2).
%F A164589 E.g.f.: (1/4)*exp(x)*(4*cosh(2*sqrt(2)*x) + 3*sqrt(2)*sinh(2*sqrt(2)*x)). - _G. C. Greubel_, Aug 12 2017
%t A164589 CoefficientList[Series[(1+2x)/(1-2x-7x^2),{x,0,30}],x] (* or *) LinearRecurrence[{2,7},{1,4},30] (* _Harvey P. Dale_, Jun 22 2011 *)
%o A164589 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+3*r)*(1+2*r)^n+(4-3*r)*(1-2*r)^n)/8: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 24 2009
%o A164589 (PARI) Vec((1+2*x)/(1-2*x-7*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Jul 16 2011
%Y A164589 Cf. A086347, A096886.
%K A164589 nonn,easy
%O A164589 0,2
%A A164589 Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009
%E A164589 Edited and extended beyond a(5) by _Klaus Brockhaus_ and _R. J. Mathar_, Aug 24 2009