A145509 a(n+1) = a(n)^2 + 2*a(n) - 2 and a(1) = 9.

9, 97, 9601, 92198401, 8500545331353601, 72259270930397519221389558374401, 5221402235392591963136699520829303150191924374488750728808857601

Offset

1,1

Comments

See A145502 for a general formula for a(n+1) = a(n)^2 + 2*a(n) - 2 and a(1) = k-1.

Links

Jason Yuen, Table of n, a(n) for n = 1..10

Formula

From Peter Bala, Nov 12 2012: (Start)

a(n) = alpha^(2^(n-1)) + (1/alpha)^(2^(n-1)) - 1, where alpha = 5 + 2*sqrt(6).

a(n) == 1 (mod 8).

Recurrence: a(n) = 11*(Product_{k = 1..n-1} a(k)) - 2 with a(1) = 9.

Product_{n >= 1} (1 + 1/a(n)) = 11/sqrt(96).

Product_{n >= 1} (1 + 2/(a(n) + 1)) = sqrt(3/2). (End)

Mathematica

aa = {}; k = 9; Do[AppendTo[aa, k]; k = k^2 + 2 k - 2, {n, 1, 10}]; aa
(* or *)
k = 10; Table[Floor[((k + Sqrt[k^2 - 4])/2)^(2^(n - 1))], {n, 1, 7}]
NestList[#^2+2#-2&, 9, 10] (* Harvey P. Dale, Jul 02 2017 *)

Crossrefs

Cf. A145502-A145510.

Sequence in context: A293986 A380639 A123821 * A098782 A076758 A085868

Adjacent sequences: A145506 A145507 A145508 * A145510 A145511 A145512

Keyword

nonn,easy

Author

Artur Jasinski, Oct 11 2008

Status

approved