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%I #11 Nov 21 2013 12:50:09
%S 1,1,5,13,29,10,76,1736,4660,548336,29284676,11332669880,
%T 83479779988156,1588027776066548704,3951095430355142456915900,
%U 559704716364298877070828931075144,29061471629068026188294896544835477139588124,10492921417426945424117408776017371634826648342796156209040
%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 numerators.
%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;
%t Numerator/@RecurrenceTable[{a[0]==a[1]==1,a[n]==(4+a[n-1])/ (1+a[n-2])},a[n],{n,20}] (* _Harvey P. Dale_, May 08 2011 *)
%Y Cf. A189486.
%K nonn,frac
%O 0,3
%A _N. J. A. Sloane_, Apr 23 2011