login
A120031
Numerators of reduced forms of fractions obtained by performing the first n divisions shown below.
30
1, 1, 2, 5, 40, 4, 48, 312, 1664, 14144, 56576, 28288, 226304, 217600, 870400, 2524160, 80773120, 2375680, 1900544, 35160064, 1406402560, 28831252480, 115325009920, 288312524800, 4613000396800, 92260007936, 369040031744
OFFSET
0,3
COMMENTS
1
-------
2*3
..-----
..4*5
....---
....6*.....
In other words, the successive fractions are
1,
1
-,
2
1..4
----,
.23.
1..45.
------,
.23..6
1..45..8
--------,
.23..67.
and so on
Suggested by a question from Ciprian Bonciocat (6 years old).
FORMULA
a(n) = numerator of x(n) where x(0)=1, x(2n+1) = x(2n) (4n+1)/(4n+2), x(2n+2) = x(2n+1)(4n+4)/(4n+3). - Matthew Conroy Jun 26 2006
EXAMPLE
1, 1/2, 2/3, 5/9, 40/63, 4/7, ...
MATHEMATICA
a[0] = 1; a[n_] := a[n] = a[n - 1] If[OddQ[n], (2 n - 1)/(2 n), (2 n)/(2 n - 1)]; A120031[n_] := Numerator[a[n]]; Array[A120031, 26] (* JungHwan Min, Nov 08 2016 *)
CROSSREFS
Cf. A120032.
Sequence in context: A183255 A307141 A109003 * A110066 A155176 A127974
KEYWORD
nonn,frac
AUTHOR
Mihai Cipu (mihai.cipu(AT)imar.ro), Jun 05 2006
EXTENSIONS
More terms from Matthew Conroy, Jun 26 2006
STATUS
approved