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 A145509 #12 Jun 02 2025 00:39:58
%S A145509 9,97,9601,92198401,8500545331353601,72259270930397519221389558374401,
%T A145509 5221402235392591963136699520829303150191924374488750728808857601
%N A145509 a(n+1)=a(n)^2+2*a(n)-2 and a(1)=9.
%C A145509 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 A145509 From Peter Bala, Nov 12 2012: (Start)
%F A145509 a(n) = alpha^(2^(n-1)) + (1/alpha)^(2^(n-1)) - 1, where alpha := 5 + 2*sqrt(6). a(n) = 1 (mod 8).
%F A145509 Recurrence: a(n) = 11*{product {k = 1..n-1} a(k)} - 2 with a(1) = 9.
%F A145509 Product {n = 1..inf} (1 + 1/a(n)) = 11/sqrt(96).
%F A145509 Product {n = 1..inf} (1 + 2/(a(n) + 1)) = sqrt(3/2).
%F A145509 (End)
%t A145509 aa = {}; k = 9; Do[AppendTo[aa, k]; k = k^2 + 2 k - 2, {n, 1, 10}]; aa
%t A145509 or
%t A145509 k =8; Table[Floor[((k + Sqrt[k^2 + 4])/2)^(2^(n - 1))], {n, 2, 7}] (*Artur Jasinski*)
%t A145509 NestList[#^2+2#-2&,9,10] (* _Harvey P. Dale_, Jul 02 2017 *)
%Y A145509 A145502-A145510.
%K A145509 nonn,easy
%O A145509 1,1
%A A145509 _Artur Jasinski_, Oct 11 2008