A144745 Recurrence sequence a(n)=a(n-1)^2-a(n-1)-1, a(0)=9.

9, 71, 4969, 24685991, 609398126966089, 371366077149776919833628989831, 137912763257614063309949706968500684963726537144819872418729

Offset: 0

Author

Artur Jasinski, Sep 20 2008

Keywords

• nonn

Comments

The original version of this sequence had a(0)=5=A144743(1) and therefore was essentially the same as that sequence A144743.

The next term a(8) has 119 digits.

Crossrefs

Cf. A000058, A082732, A144743, A144744, A144746, A144747, A144748.

Programs

Mathematica

k = 9; a = {k}; Do[k = k^2 - k - 1; AppendTo[a, k], {n, 1, 10}]; a
NestList[#^2 - # - 1 &, 9, 7]  (* Harvey P. Dale, Feb 04 2011 *)

PARI

a(n,s=9)=for(i=1,n,s=s^2-s-1);s \\ M. F. Hasler, Oct 06 2014

Formula

a(n) = a(n-1)^2-a(n-1)-1 and a(0)=9.

a(n) ~ c^(2^n), where c = 8.395688554881795978328174160925857176207363473280394010762212170489... . - Vaclav Kotesovec, May 06 2015

Extensions

New initial value a(0)=9 from M. F. Hasler, Oct 20 2014