OFFSET
1,5
COMMENTS
Expected area of the convex hull of n points picked at random inside a triangle with unit area.
LINKS
Robert Israel, Table of n, a(n) for n = 1..2296
Eric Weisstein's World of Mathematics, Triangle Point Picking
Eric Weisstein's World of Mathematics, Simplex Simplex Picking
EXAMPLE
0, 0, 1/12, 1/6, 43/180, 3/10, 197/560, 499/1260, 5471/12600, ...
MAPLE
h:= 1:
A[1]:= 0:
for n from 2 to 50 do
h:= h+1/n;
A[n]:= numer(1-2*h/(n+1));
od:
seq(A[i], i=1..50); # Robert Israel, Oct 17 2018
MATHEMATICA
Table[Numerator[1-2HarmonicNumber[n]/(n+1)], {n, 30}] (* Harvey P. Dale, Oct 10 2013 *)
PROG
(PARI) a(n) = numerator(1-2*sum(i=1, n, 1/i)/(n+1)) \\ Felix Fröhlich, Oct 17 2018
CROSSREFS
KEYWORD
nonn,frac,changed
AUTHOR
Eric W. Weisstein, Apr 15 2004
STATUS
approved