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.

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

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

Cf. A229839, A246918, A246919.

Sequence in context: A214574 A342510 A298071 * A244964 A096993 A297774

Adjacent sequences: A246917 A246918 A246919 * A246921 A246922 A246923

Keyword

nonn

Author

Colin Barker, Sep 07 2014

Status

approved