A074935 Denominator of a(n), where for n > 2, a(n)=-1/a(n-1)+1/a(n-2), a(1)=1, a(2)=2.

1, 1, 2, 2, 3, 24, 200, 6675, 3045936, 46360115600, 251445391554623475, 23318100352452485482468409184

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).

Links

Table of n, a(n) for n=1..12.

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.

Sequence in context: A189254 A036503 A109590 * A320103 A212796 A078239

Adjacent sequences: A074932 A074933 A074934 * A074936 A074937 A074938

Keyword

nonn,frac

Author

Zak Seidov, Oct 24 2002

Status

approved