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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, 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.
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: A193232 A375545 A336841 * A131758 A095909 A151872
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Apr 23 2011
STATUS
approved