A100701 a(n) = a(n-1) + a(n-2) + a(n-1)*a(n-2) for n>=2; a(0)=2, a(1)=3.

2, 3, 11, 47, 575, 27647, 15925247, 440301256703, 7011906707722862591, 3087351335301583621409910816767, 21648219537098310851336266290644502090473753542655

Offset: 0

Author

Parthasarathy Nambi, Dec 09 2004

Keywords

• nonn

Comments

In general, if b(n) is defined recursively by b(0) = p, b(1) = q, b(n) = b(n-1) + b(n-2) + b(n-1) * b(n-2) for n >= 2 then b(n) = p^Fibonacci(n-1) * q^Fibonacci(n) - 1. - Rahul Goswami, Apr 15 2020

Examples

			a(2) = (2 + 3) + 2*3 = 11.
		

Crossrefs

Cf. A000045 (Fibonacci), A063896.

Programs

Mathematica

a=2;b=3;lst={a,b};Do[c=a*b+a+b;AppendTo[lst,c];a=b;b=c,{n,2*3!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 05 2009 *)

PARI

a(n)={3^fibonacci(n-1) * 4^fibonacci(n) - 1} \\ Andrew Howroyd, Apr 14 2020

Formula

a(n) = a(n-1) + a(n-2) + a(n-1)*a(n-2) with a(0)=2 and a(1)=3.

a(n) = 3^Fibonacci(n-1) * 4^Fibonacci(n) - 1. - Rahul Goswami, Apr 15 2020

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Sep 05 2009