A143684 a(0) = a(1) = 0; thereafter a(n) = 2*a(n-1)*a(n-2) + 1.

0, 0, 1, 1, 3, 7, 43, 603, 51859, 62541955, 6486726488691, 811385112306041061811, 10526466601050236861337066646958803, 17082036570557873538131893815781561362696563088187144467, 359626974875792367278553795120318710475396935851854517275793126801351587742904492716786003

Offset: 0

Author

N. J. A. Sloane, based on email from Carla J. Garner-Bennett, Nov 13 2008

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..19
• A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
• A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)

Crossrefs

Cf. A000058, A007660, A142471.

Programs

Magma

I:=[0,0]; [n le 2 select I[n] else 2*Self(n-1)*Self(n-2)+1: n in [1..15]]; // Vincenzo Librandi, Nov 14 2011

Mathematica

a[n_]:=a[n]=If[n<2,0, 2*a[n-1]*a[n-2]+1]; Table[a[n], {n,0,15}] (* G. C. Greubel, May 29 2021 *)

Sage

def a(n): return 0 if (n<2) else 2*a(n-1)*a(n-2) + 1
[a(n) for n in (0..10)] # G. C. Greubel, May 29 2021

Formula

Equals A142471/2.

a(n) is about 1/2*c^(phi^n), where c = 1.27817816239858832577... and phi is the golden ratio. - Charles R Greathouse IV, Mar 21 2012, corrected by Vaclav Kotesovec, May 05 2015