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%I #7 Jul 21 2019 11:26:26
%S 1,1,2,2,3,24,200,6675,3045936,46360115600,251445391554623475,
%T 23318100352452485482468409184
%N Denominator of a(n), where for n > 2, a(n)=-1/a(n-1)+1/a(n-2), a(1)=1, a(2)=2.
%C a(n)->-(-1)^n sqrt(2), a slowly converging sequence. In general, for recursive sequence: a(n)=Sum[i=1,...,k<n,c(i)/a(i)], asymptotic solution is: a(n)-> +/- Sqrt[Sum[i=1,..,k,abs[c(i)]]], independently on initial a(i).
%F a(n>2)=-1/a(n-1)+1/a(n-2), a(1)=1, a(2)=2, a(n)->-(-1)^n sqrt(2).
%e a(3)=-1/a(2)+1/a(1)=-1/2+1=1/2, therefore in the sequence, 3rd term is 2.
%t RecurrenceTable[{a[1]==1,a[2]==2,a[n]==-1/a[n-1]+1/a[n-2]},a,{n,13}]// Denominator (* _Harvey P. Dale_, Jul 21 2019 *)
%Y Cf. A076655.
%K nonn,frac
%O 1,3
%A _Zak Seidov_, Oct 24 2002
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