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 A219163 #18 Dec 11 2022 06:09:39
%S A219163 4,194,1416317954,4023861667741036022825635656102100994
%N A219163 Recurrence equation a(n+1) = a(n)^4 - 4*a(n)^2 + 2 with a(0) = 4.
%C A219163 Bisection of A003010.
%C A219163 a(4) has 147 digits and a(5) has 586 digits. - _Harvey P. Dale_, Mar 03 2020
%F A219163 Let alpha = 2 + sqrt(3). Then a(n) = (alpha)^(4^n) + (1/alpha)^(4^n).
%F A219163 a(n) = A003010(2*n) = A003500(4^n).
%F A219163 Product_{n >= 0} ((1 + 2/a(n))/(1 - 2/a(n)^2)) = sqrt(3).
%F A219163 From _Peter Bala_, Dec 06 2022: (Start)
%F A219163 a(n) = 2*T(4^n,2), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind.
%F A219163 Let b(n) = a(n) - 4. The sequence {b(n)} appears to be a strong divisibility sequence, that is, gcd(b(n),b(m)) = b(gcd(n,m)) for n, m >= 1. (End)
%t A219163 NestList[#^4-4#^2+2&,4,5] (* _Harvey P. Dale_, Mar 03 2020 *)
%o A219163 (PARI) a(n)={if(n==0,4,a(n-1)^4-4*a(n-1)^2+2)} \\ _Edward Jiang_, Sep 11 2014
%Y A219163 Cf. A001999, A003010, A003500, A219162, A219164, A219165.
%K A219163 nonn,easy
%O A219163 0,1
%A A219163 _Peter Bala_, Nov 13 2012