A145507 a(n+1) = a(n)^2 + 2*a(n) - 2 and a(1) = 7.

7, 61, 3841, 14760961, 217885999165441, 47474308632322991920487055361, 2253809980117057347661794063813616885861274573005652951041

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..11

Formula

From Peter Bala, Nov 12 2012: (Start)

a(n) = alpha^(2^(n-1)) + (1/alpha)^(2^(n-1)) - 1, where alpha = 4 + sqrt(15).

a(n) = 2*A005828(n-1) - 1.

Recurrence: a(n) = 9*(Product_{k = 1..n-1} a(k)) - 2 with a(1) = 7.

Product_{n >= 1} (1 + 1/a(n)) = (3/10)*sqrt(15).

Product_{n >= 1} (1 + 2/(a(n) + 1)) = sqrt(5/3). (End)

Mathematica

aa = {}; k = 7; Do[AppendTo[aa, k]; k = k^2 + 2 k - 2, {n, 1, 10}]; aa
(* Alternative: *)
k = 8; Table[Floor[((k + Sqrt[k^2 - 4])/2)^(2^(n - 1))], {n, 1, 7}]

Crossrefs

Cf. A145502-A145510, A005828.

Sequence in context: A048287 A391954 A317430 * A254121 A047685 A171078

Adjacent sequences: A145504 A145505 A145506 * A145508 A145509 A145510

Keyword

nonn,changed

Author

Artur Jasinski, Oct 11 2008

Status

approved