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 A145508 #12 Jun 02 2025 00:39:52
%S A145508 8,78,6238,38925118,1515164889164158,2295724641355838227053650177278,
%T A145508 5270351628928392053240255925779522360603268430188068127843838
%N A145508 a(n+1)=a(n)^2+2*a(n)-2 and a(1)=8.
%C A145508 General formula for a(n+1)=a(n)^2+2*a(n)-2 and a(1)=k+1 is a(n)=Floor[((k + Sqrt[k^2 + 4])/2)^(2^((n+1) - 1))
%F A145508 From Peter Bala, Nov 12 2012: (Start)
%F A145508 a(n) = alpha^(2^(n-1)) + (1/alpha)^(2^(n-1)) - 1, where alpha := 1/2*(9 + sqrt(77)). a(n) = 1 (mod 7).
%F A145508 Recurrence: a(n) = 10*{product {k = 1..n-1} a(k)} - 2 with a(1) = 8.
%F A145508 Product {n = 1..inf} (1 + 1/a(n)) = 10/sqrt(77).
%F A145508 Product {n = 1..inf} (1 + 2/(a(n) + 1)) = sqrt(11/7).
%F A145508 (End)
%t A145508 aa = {}; k = 8; Do[AppendTo[aa, k]; k = k^2 + 2 k - 2, {n, 1, 10}]; aa
%t A145508 or
%t A145508 k =7; Table[Floor[((k + Sqrt[k^2 + 4])/2)^(2^(n - 1))], {n, 2, 7}] (*Artur Jasinski*)
%t A145508 NestList[#^2+2#-2&,8,8] (* _Harvey P. Dale_, Sep 20 2013 *)
%Y A145508 A145502-A145510.
%K A145508 nonn,easy
%O A145508 1,1
%A A145508 _Artur Jasinski_, Oct 11 2008