A144747 Recurrence sequence a(n)=a(n-1)^2-a(n-1)-1, a(0)=7.

7, 41, 1639, 2684681, 7207509387079, 51948191564824694742765161, 2698614606855723567054656642857156538246857652590759, 7282520796335071470236496456671241855257664867148949932302276253455702665493855273950765616767079605321

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, A144748.

Programs

Mathematica

a = {}; k = 7; Do[k = k^2 - k - 1; AppendTo[a, k], {n, 1, 10}]; a

PARI

a(n, s=7)={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)=7.

a(n) ~ c^(2^n), where c = 6.3622623884585267364822329679498420997632627444610172910703030892754... . - Vaclav Kotesovec, May 06 2015

Extensions

Edited by M. F. Hasler, Oct 06 2014