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A045529 a(n+1) = 5*a(n)^3 - 3*a(n). 27
1, 2, 34, 196418, 37889062373143906, 271964099255182923543922814194423915162591622175362 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The next term, a(6), has 153 digits. - Harvey P. Dale, Oct 24 2011

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..7

FORMULA

a(n) = Fibonacci(3^n). - Leroy Quet, Mar 17 2002

The first example I know in which a(n) can be expressed as (4/5)^(1/2)*cosh(3^n*argch((5/4)^(1/2)).

a(n+1) = a(n)*A002814(n+1). - Lekraj Beedassy, Jun 16 2003

a(n) = (G^(3^n) - (1 - G)^(3^n))/Sqrt[5] where G = GoldenRatio = (1 + Sqrt[5])/2. - Artur Jasinski, Oct 05 2008

a(n)=(4/5)^(1/2)*cosh((3^n)*arccosh((5/4)^(1/2)). - Artur Jasinski, Oct 05 2008

MATHEMATICA

G = (1 + Sqrt[5])/2; Table[Expand[(G^(3^n) - (1 - G)^(3^n))/Sqrt[5]], {n, 1, 7}] (* Artur Jasinski, Oct 05 2008 *)

Table[Round[(4/5)^(1/2)*Cosh[3^n*ArcCosh[((5/4)^(1/2))]]], {n, 1, 4}] (* Artur Jasinski, Oct 05 2008 *)

RecurrenceTable[{a[0]==1, a[n]==5a[n-1]^3-3a[n-1]}, a[n], {n, 6}] (* Harvey P. Dale, Oct 24 2011 *)

NestList[5#^3-3#&, 1, 5] (* Harvey P. Dale, Dec 21 2014 *)

PROG

(Maxima) A045529(n):=fib(3^n)$

makelist(A045529(n), n, 0, 10); /* Martin Ettl, Nov 12 2012 */

CROSSREFS

Cf. (k^n)-th Fibonacci number: A058635 (k=2), this sequence (k=3), A145231 (k=4), A145232 (k=5), A145233 (k=6), A145234 (k=7), A250487 (k=8), A250488 (k=9), A250489 (k=10).

Sequence in context: A002782 A155205 A230244 * A293245 A077747 A041012

Adjacent sequences:  A045526 A045527 A045528 * A045530 A045531 A045532

KEYWORD

nonn

AUTHOR

Jose Eduardo Blazek

STATUS

approved

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Last modified February 22 23:32 EST 2018. Contains 299472 sequences. (Running on oeis4.)