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A145509 a(n+1)=a(n)^2+2*a(n)-2 and a(1)=9 0
9, 97, 9601, 92198401, 8500545331353601, 72259270930397519221389558374401, 5221402235392591963136699520829303150191924374488750728808857601 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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))

LINKS

Table of n, a(n) for n=1..7.

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..inf} (1 + 1/a(n)) = 11/sqrt(96).

Product {n = 1..inf} (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 =8; Table[Floor[((k + Sqrt[k^2 + 4])/2)^(2^(n - 1))], {n, 2, 7}] (*Artur Jasinski*)

NestList[#^2+2#-2&, 9, 10] (* Harvey P. Dale, Jul 02 2017 *)

CROSSREFS

A145502-A145510.

Sequence in context: A218500 A293986 A123821 * A098782 A076758 A085868

Adjacent sequences:  A145506 A145507 A145508 * A145510 A145511 A145512

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Oct 11 2008

STATUS

approved

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Last modified November 15 18:59 EST 2019. Contains 329149 sequences. (Running on oeis4.)