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 A164603 #23 Jul 07 2025 16:16:57
%S A164603 1,18,76,376,1808,8736,42176,203648,983296,4747776,22924288,110688256,
%T A164603 534450176,2580553728,12460015616,60162277376,290489171968,
%U A164603 1402605797376,6772379877376,32699942699008,157889290305536
%N A164603 a(n) = ((1+4*sqrt(2))*(2+2*sqrt(2))^n + (1-4*sqrt(2))*(2-2*sqrt(2))^n)/2.
%C A164603 Binomial transform of A164602. Second binomial transform of A164702. Inverse binomial transform of A164604.
%H A164603 G. C. Greubel, <a href="/A164603/b164603.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..164 from Vincenzo Librandi)
%H A164603 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,4).
%F A164603 a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 18.
%F A164603 G.f.: (1+14*x)/(1-4*x-4*x^2).
%F A164603 E.g.f.: exp(2*x)*( cosh(2*sqrt(2)*x) + 4*sqrt(2)*sinh(2*sqrt(2)*x) ). - _G. C. Greubel_, Aug 11 2017
%t A164603 CoefficientList[Series[(-1-14 n)/(-1+4 n+4 n^2),{n,0,20}],n] (* _Harvey P. Dale_, Feb 22 2011 *)
%o A164603 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+4*r)*(2+2*r)^n+(1-4*r)*(2-2*r)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 23 2009
%o A164603 (PARI) Vec((1+14*x)/(1-4*x-4*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Jun 12 2011
%Y A164603 Cf. A164602, A164702, A164604.
%K A164603 nonn,easy
%O A164603 0,2
%A A164603 Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009
%E A164603 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 23 2009