This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A096655 #8 Jul 26 2015 01:56:02
%S A096655 1,1,3,11,64,567,7883,172914,6044619,338333121,30444101814,
%T A096655 4414062308985,1032860468654721,390416873200823322,
%U A096655 238543681049185056237,235680767488198152732339
%N A096655 a(n) = F(n+1)*a(n-1) + F(n)*a(n-2), where F = A000045 (Fibonacci numbers), a(0)=1, a(1)=1.
%C A096655 If the initial values are changed to a(0)=1 and a(1)=2, the resulting sequence (p(0),p(1),...)=(1,2,5,19,....) is essentially A089126. Writing A096655 as (q(0),q(1),...), the quotients p(n)/q(n) are the self-convergents to the number 1.719525... whose self-continued fraction is (1,1,2,3,5,...)=A000045. For definitions, see A096654. Now writing A096655 as (p(0),p(1),...) and A096656 as (q(0),q(1),...), the quotients p(n)/q(n) are the self-convergents to the number 1.389805... whose self-continued fraction is (1,2,3,5,...).
%F A096655 a(n) is asymptotic to c*phi^(n(n+1)/2)/5^(n/2) where c=3.487197183858494166192... and phi is the golden ratio. - _Benoit Cloitre_, Jul 02 2004
%e A096655 a(2) = F(3)*1 + F(2)*1 = 3, a(3) = F(4)*3 + F(3)*1 = 11.
%t A096655 a[0] = 1; a[1] = 1; a[n_] := Fibonacci[n + 1]*a[n - 1] + Fibonacci[n]*a[n - 2]; Table[ a[n], {n, 0, 16}] (* _Robert G. Wilson v_, Jul 09 2004 *)
%Y A096655 Cf. A000045, A089126, A096654.
%K A096655 nonn
%O A096655 0,3
%A A096655 _Clark Kimberling_, Jul 01 2004
%E A096655 More terms from _Benoit Cloitre_, Jul 02 2004