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 A163613 #6 Sep 08 2022 08:45:46
%S A163613 1,8,30,104,356,1216,4152,14176,48400,165248,564192,1926272,6576704,
%T A163613 22454272,76663680,261746176,893657344,3051137024,10417233408,
%U A163613 35566659584,121432171520,414595366912,1415517124608,4832877764608
%N A163613 a(n) = ((1 + 3*sqrt(2))*(2 + sqrt(2))^n + (1 - 3*sqrt(2))*(2 - sqrt(2))^n)/2.
%C A163613 Binomial transform of A048694. Second binomial transform of A163864. Inverse binomial transform of A163614.
%H A163613 G. C. Greubel, <a href="/A163613/b163613.txt">Table of n, a(n) for n = 0..1000</a>
%H A163613 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2).
%F A163613 a(n) = 4*a(n-1) - 2*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
%F A163613 G.f.: (1+4*x)/(1-4*x+2*x^2).
%F A163613 E.g.f.: exp(2*x)*( cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Jul 30 2017
%t A163613 LinearRecurrence[{4, -2}, {1, 8}, 50] (* _G. C. Greubel_, Jul 30 2017 *)
%o A163613 (Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(2+r)^n+(1-3*r)*(2-r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 06 2009
%o A163613 (PARI) x='x+O('x^50); Vec((1+4*x)/(1-4*x+2*x^2)) \\ _G. C. Greubel_, Jul 30 2017
%Y A163613 Cf. A048694, A163864 (1, 6, 2, 12, 4, 24, ...), A163614.
%K A163613 nonn
%O A163613 0,2
%A A163613 Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
%E A163613 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 06 2009