A145504 a(n+1) = a(n)^2 + 2*a(n) - 2 and a(1) = 4.

4, 22, 526, 277726, 77132286526, 5949389624883225721726, 35395236908668169265765137996816180039862526, 1252822795820745419377249396736955608088527968701950139470082687906021780162741058825726

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.

The next term (a(9)) has 175 digits. - Harvey P. Dale, Nov 16 2013

Links

Jason Yuen, Table of n, a(n) for n = 1..11

Formula

From Peter Bala, Nov 12 2012: (Start)

a(n) = alpha^(2^(n-1)) + (1/alpha)^(2^(n-1)) - 1, where alpha = 1/2*(5 + sqrt(21)).

a(n) = A003487(n-1) - 1.

Recurrence: a(n) = 6*(Product_{k = 1..n-1} a(k)) - 2 with a(1) = 4.

Product_{n>=1} (1 + 1/a(n)) = (2/7)*sqrt(21).

Product_{n>=1} (1 + 2/(a(n) + 1)) = sqrt(7/3). (End)

Mathematica

NestList[#^2+2#-2&, 4, 7] (* Harvey P. Dale, Nov 16 2013 *)

Crossrefs

Cf. A145502-A145510, A003487.

Sequence in context: A053722 A336212 A276122 * A321604 A276124 A104166

Adjacent sequences: A145501 A145502 A145503 * A145505 A145506 A145507

Keyword

nonn

Author

Artur Jasinski, Oct 11 2008

Extensions

One additional term (a(8)) from Harvey P. Dale, Nov 16 2013

Status

approved