OFFSET
1,5
COMMENTS
A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).
A nontrivial cevian is one that does not coincide with a side of the triangle.
For an equilateral triangle of side n, the lengths of its cevians are the values of y in the solutions to x^2-y^2-n*x+n^2=0.
LINKS
Colin Barker, Table of n, a(n) for n = 1..10000
Wikipedia, Cevian
EXAMPLE
a(15) = 5 because cevians of an equilateral triangle of side 15 have length 13, 21, 35, 57 or 169.
PROG
(PARI)
\\ Returns the number of cevians of an equilateral triangle of side n.
count(n) = {
s=[];
n=12*n^2;
fordiv(n, f,
g=n\f;
if(f<=g && (f+g)%2==0,
x=(f+g)\2;
if(x%4==0,
s=concat(s, x\4)
)
)
);
Colrev(s)~
}
vector(100, n, #count(n)-1)
CROSSREFS
KEYWORD
nonn
AUTHOR
Colin Barker, Sep 07 2014
STATUS
approved