OFFSET
3,2
COMMENTS
Geometric Interpretation: Given n-sided regular polygon "rolling" on a flat surface with constant angular velocity, a(n) is the numerator of the ratio:
[("time" taken for any one vertex to move from highest point to lowest point) / ("time" taken for polygon to finish one complete turn)] := b(n).
Lim_{n->infinity} b(n) = 1/2 (can be easily proven).
LINKS
Luca Alexander, about 100000 terms
FORMULA
a(n) = numerator((n - 1) / (2*n)) for even n; a(n) = numerator((2*n - 3) / (4*n)) for odd n.
EXAMPLE
For n = 3, a(3) = numerator of ((2*3-3)/4*n) = numerator of (3/12) = numerator of (1/4) = 1.
MATHEMATICA
Array[Numerator[(2 (# - 1) - Mod[#, 2])/(4 #)] &, 66, 3] (* Michael De Vlieger, Oct 06 2019 *)
PROG
(PARI) a(n) = {numerator((2*(n-1) - n%2)/(4*n))} \\ Andrew Howroyd, Oct 06 2019
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Luca Alexander, Oct 06 2019
STATUS
approved