A145452 a(n) = (1/(10*sqrt(2)))*((1 + sqrt(2))^(3^n) - (1 - sqrt(2))^(3^n)).

1, 197, 1529074009, 715015595589726925478809323773, 73109958817558064847374518951460268418149511794461927024546978118655493358310911623870212081

Offset: 1

Author

Artur Jasinski, Oct 10 2008

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..7

Crossrefs

Cf. A000129, A006266, A145451.

Programs

Magma

[Evaluate(DicksonSecond(3^n -1, -1), 2)/5: n in [1..6]]; // G. C. Greubel, Mar 25 2022

Mathematica

Table[Simplify[Expand[(1/(10Sqrt[2]))((1+Sqrt[2])^(3^n) + (1-Sqrt[2])^(3^n))]], {n,5}]
Fibonacci[3^Range[6], 2]/5 (* G. C. Greubel, Mar 25 2022 *)

Sage

[lucas_number1(3^n,2,-1)/5 for n in (1..6)] # G. C. Greubel, Mar 25 2022

Formula

a(n) = (1/(10*sqrt(2)))*((1 + sqrt(2))^(3^n) - (1 - sqrt(2))^(3^n)).

a(n+1) = 200*a(n)^3 - 3*a(n), a(1) = 1.

a(n) = A000129(3^n)/5 . - R. J. Mathar, Jan 18 2021

Extensions

Offset corrected by R. J. Mathar, Jan 18 2021