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A045529 a(n+1) = 5*a(n)^3 - 3*a(n). 28

%I

%S 1,2,34,196418,37889062373143906,

%T 271964099255182923543922814194423915162591622175362

%N a(n+1) = 5*a(n)^3 - 3*a(n).

%C The next term, a(6), has 153 digits. - _Harvey P. Dale_, Oct 24 2011

%H Seiichi Manyama, <a href="/A045529/b045529.txt">Table of n, a(n) for n = 0..7</a>

%F a(n) = Fibonacci(3^n). - _Leroy Quet_, Mar 17 2002

%F 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)).

%F a(n+1) = a(n)*A002814(n+1). - _Lekraj Beedassy_, Jun 16 2003

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

%F a(n)=(4/5)^(1/2)*cosh((3^n)*arccosh((5/4)^(1/2)). - _Artur Jasinski_, Oct 05 2008

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

%t Table[Round[(4/5)^(1/2)*Cosh[3^n*ArcCosh[((5/4)^(1/2))]]], {n, 1, 4}] (* _Artur Jasinski_, Oct 05 2008 *)

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

%t NestList[5#^3-3#&,1,5] (* _Harvey P. Dale_, Dec 21 2014 *)

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

%o makelist(A045529(n),n,0,10); /* _Martin Ettl_, Nov 12 2012 */

%Y 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).

%K nonn

%O 0,2

%A _Jose Eduardo Blazek_

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Last modified November 14 04:47 EST 2019. Contains 329108 sequences. (Running on oeis4.)