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 A242232 #12 Jun 12 2025 15:50:35
%S A242232 6,71,10081,203253121,82623662392481281,
%T A242232 13653339174293451118767199870801921,
%U A242232 372827341216592355174245573447441869623455324379507680549087234580481
%N A242232 a(n) = 2*a(n-1)^2 - 1, a(0)=6.
%C A242232 In general, for a(0)=p is a(n) = cosh(2^n*arccosh(p)) = (1/2)*(p+sqrt(p^2-1))^(2^n) + (1/2)*(p+sqrt(p^2-1))^(-2^n).
%F A242232 a(n) = (1/2)*(6+sqrt(35))^(2^n) + (1/2)*(6+sqrt(35))^(-2^n).
%F A242232 a(n) = A023038(2^n).
%F A242232 a(n) = T(2^n,6), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind. - _Peter Bala_, Mar 30 2022
%t A242232 RecurrenceTable[{a[n+1]==2*a[n]^2-1,a[0]==6},a,{n,0,10}]
%t A242232 NestList[2#^2-1&,6,10] (* _Harvey P. Dale_, Jun 12 2025 *)
%Y A242232 Cf. A002812, A001601, A005828, A084765.
%K A242232 nonn
%O A242232 0,1
%A A242232 _Vaclav Kotesovec_, May 08 2014