%I A057677
%S A057677 1,2,3,7,32,339,14287,6877760,143806067571,1372321205281802503,
%T A057677 277081140489649960447116859520,
%U A057677 544875880027767543589801386360499677678401262339
%N A057677 a(n) is the numerator of b(n) where b(n)=1/b(n-1)+1/b(n-2) with b(1)=1 
               and b(2)=2.
%C A057677 lim_{n->infty} b(n)=sqrt(2) with geometric convergence since abs(b(n)-sqrt(2))<2*2^(-n/
               2)
%F A057677 a(n) satisfies the cubic recurrence : a(1)=1, a(2)=2, a(3)=3, a(4)=7, 
               a(5)=32 and for n>=6 a(n)=a(n-2)^2*a(n-3)+a(n-1)*a(n-3)*a(n-4)
%F A057677 lim_{n->infty} b(n)=sqrt(2) with geometric convergence since abs(b(n)-sqrt(2))<2*2^(-n/
               2)
%Y A057677 Cf. A066932.
%Y A057677 Sequence in context: A096350 A018239 A066279 this_sequence A032148 A101484 
               A004026
%Y A057677 Adjacent sequences: A057674 A057675 A057676 this_sequence A057678 A057679 
               A057680
%K A057677 nonn,frac
%O A057677 1,2
%A A057677 Zak Seidov (zakseidov(AT)yahoo.com), Oct 24 2002
%E A057677 Edited by Benoit Cloitre, Oct 25 2005