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A246920 The number of distinct lengths of nontrivial integral cevians of an equilateral triangle of side n that divide an edge into two integral parts. 4
0, 0, 1, 0, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 5, 4, 2, 2, 2, 2, 5, 2, 2, 5, 4, 2, 3, 2, 2, 5, 2, 6, 5, 2, 8, 2, 2, 2, 5, 8, 2, 5, 2, 2, 8, 2, 2, 9, 4, 4, 5, 2, 2, 3, 8, 8, 5, 2, 2, 5, 2, 2, 8, 8, 8, 5, 2, 2, 5, 8, 2, 8, 2, 2, 9, 2, 8, 5, 2, 14, 4, 2, 2, 5, 8, 2 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A214574 A342510 A298071 * A244964 A096993 A297774
KEYWORD
nonn
AUTHOR
Colin Barker, Sep 07 2014
STATUS
approved

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Last modified April 18 06:24 EDT 2024. Contains 371769 sequences. (Running on oeis4.)