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

%I

%S 2,3,11,47,575,27647,15925247,440301256703,7011906707722862591,

%T 3087351335301583621409910816767,

%U 21648219537098310851336266290644502090473753542655

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

%C 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

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

%F a(n) = 3^Fibonacci(n-1) * 4^Fibonacci(n) - 1. - _Rahul Goswami_, Apr 15 2020

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

%t 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 *)

%o (PARI) a(n)={3^fibonacci(n-1) * 4^fibonacci(n) - 1} \\ _Andrew Howroyd_, Apr 14 2020

%Y Cf. A000045 (Fibonacci), A063896.

%K nonn

%O 0,1

%A _Parthasarathy Nambi_, Dec 09 2004

%E More terms from _Vladimir Joseph Stephan Orlovsky_, Sep 05 2009

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Last modified July 12 10:09 EDT 2020. Contains 335657 sequences. (Running on oeis4.)