login
A189485
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.
1
1, 1, 5, 13, 29, 10, 76, 1736, 4660, 548336, 29284676, 11332669880, 83479779988156, 1588027776066548704, 3951095430355142456915900, 559704716364298877070828931075144, 29061471629068026188294896544835477139588124, 10492921417426945424117408776017371634826648342796156209040
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;
MATHEMATICA
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 *)
CROSSREFS
Cf. A189486.
Sequence in context: A060182 A357945 A147066 * A226616 A226618 A321770
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Apr 23 2011
STATUS
approved