A189486 - OEIS

%I #12 Mar 30 2012 16:52:01

%S 1,1,2,4,14,7,43,731,2023,293573,16486961,5626477847,38535553135033,

%T 776247953589619099,2069276059395278540341403,

%U 288477890749068052847537054483767,14233818196730866565020787814994280535215309,5106374385967496893562303709860513496951269918036531477033

%N 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.

%D 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.

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

%p f:=proc(n) option remember;

%p if n <= 1 then 1; else (4+f(n-1))/(1+f(n-2)); fi; end;

%Y Cf. A189485.

%K nonn,frac

%O 0,3

%A _N. J. A. Sloane_, Apr 23 2011