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, 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.

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;

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

Adjacent sequences: A189482 A189483 A189484 * A189486 A189487 A189488

Keyword

nonn,frac

Author

N. J. A. Sloane, Apr 23 2011

Status

approved