A189486 Define a sequence of fractions by f(0)=f(1)=1, thereafter f(n)=(4+f(n-1))/(1+f(n-2)); sequence gives denominators.

1, 1, 2, 4, 14, 7, 43, 731, 2023, 293573, 16486961, 5626477847, 38535553135033, 776247953589619099, 2069276059395278540341403, 288477890749068052847537054483767, 14233818196730866565020787814994280535215309, 5106374385967496893562303709860513496951269918036531477033

Offset

0,3

References

Emilie Ann Hogan, Experimental Mathematics Applied to the Study of Nonlinear Recurrences, Ph. D. Dissertation, Math. Dept., Rutgers University, May 2011. See Theorem 2.4.1.

Links

Table of n, a(n) for n=0..17.

Example

1, 1, 5/2, 13/4, 29/14, 10/7, 76/43, 1736/731, 4660/2023, 548336/293573, ...

Maple

f:=proc(n) option remember;
if n <= 1 then 1; else (4+f(n-1))/(1+f(n-2)); fi; end;

Crossrefs

Cf. A189485.

Sequence in context: A325117 A193232 A336841 * A131758 A095909 A151872

Adjacent sequences: A189483 A189484 A189485 * A189487 A189488 A189489

Keyword

nonn,frac

Author

N. J. A. Sloane, Apr 23 2011

Status

approved