OFFSET
0,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Henry Bottomley, Medians and area bisectors of a triangle.
S. Ramanujan, Notebook entry.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
Sum_{i>0} 1/a(i) = log(2)*3/4 - 1/2 = 0.019860..., which is the ratio of the area of the deltoid envelope formed by area bisectors of a triangle to the area of the triangle.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Harvey P. Dale, Dec 24 2012
Sum_{n>=1} (-1)^(n+1)/a(n) = 1/2 - log(2)/4 + log(tan(Pi/8))/(2*sqrt(2)). Amiram Eldar, Mar 20 2022
EXAMPLE
a(10) = 39*40*41 = 63960.
MATHEMATICA
Table[64n^3-4n, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 60, 504, 1716}, 40] (* Harvey P. Dale, Dec 24 2012 *)
PROG
(PARI) a(n)=(4*n-1)*4*n*(4*n+1) \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, Apr 08 2002
STATUS
approved