A144748 Recurrence sequence a(n)=a(n-1)^2-a(n-1)-1, a(0)=8.

8, 55, 2969, 8811991, 77651176572089, 6029705223029665929437251831, 36357345076631233348346773693633697407708655232275600729, 1321856541021241383115043586121503961331042183698683965174269952435581223368633124721267107619465028785549730711

Offset: 0

Author

Artur Jasinski, Sep 20 2008

Keywords

• nonn

Comments

a(0)=3 is the smallest integer generating an increasing sequence of the form a(n)=a(n-1)^2-a(n-1)-1, cf. A144743.

Crossrefs

Cf. A000058, A082732, A144743, A144744, A144745, A144746, A144747.

Programs

Mathematica

a = {}; k = 8; Do[k = k^2 - k - 1; AppendTo[a, k], {n, 1, 10}]; a
NestList[#^2-#-1&,8,10] (* Harvey P. Dale, Mar 14 2016 *)

PARI

a(n, s=8)={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)=8.

a(n) ~ c^(2^n), where c = 7.3813237216360344087566795911708086794628396333350474334044779783264... . - Vaclav Kotesovec, May 06 2015

Extensions

Edited by M. F. Hasler, Oct 06 2014