A144744 Recurrence sequence a(n)=a(n-1)^2-a(n-1)-1, a(0)=4.

4, 11, 109, 11771, 138544669, 19194625169774891, 368433635408155743950638444286989, 135743343700069833946317076518699443524748244656296738254150399131

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.

Crossrefs

Cf. A000058, A082732, A144743, A144745, A144746, A144747, A144748.

Programs

Mathematica

a = {}; k = 4; Do[k = k^2 - k - 1; AppendTo[a, k], {n, 1, 10}]; a

PARI

a(n, s=4)={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)=4.

a(n) ~ c^(2^n), where c = 3.22737450272053234771396610986262048906046050824600724014923334412606964... . - Vaclav Kotesovec, May 06 2015

Extensions

Edited by M. F. Hasler, Oct 06 2014