OFFSET
1,3
COMMENTS
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).
FORMULA
a(n>2)=-1/a(n-1)+1/a(n-2), a(1)=1, a(2)=2, a(n)->-(-1)^n sqrt(2).
EXAMPLE
a(3)=-1/a(2)+1/a(1)=-1/2+1=1/2, therefore in the sequence, 3rd term is 2.
MATHEMATICA
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 *)
CROSSREFS
Cf. A076655.
KEYWORD
nonn,frac
AUTHOR
Zak Seidov, Oct 24 2002
STATUS
approved