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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.

%I A246920 #19 Dec 10 2016 19:35:57
%S A246920 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,
%T A246920 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,
%U A246920 5,8,2,8,2,2,9,2,8,5,2,14,4,2,2,5,8,2
%N 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.
%C A246920 A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).
%C A246920 A nontrivial cevian is one that does not coincide with a side of the triangle.
%C A246920 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.
%H A246920 Colin Barker, <a href="/A246920/b246920.txt">Table of n, a(n) for n = 1..10000</a>
%H A246920 Wikipedia, <a href="http://en.wikipedia.org/wiki/Cevian">Cevian</a>
%e A246920 a(15) = 5 because cevians of an equilateral triangle of side 15 have length 13, 21, 35, 57 or 169.
%o A246920 (PARI)
%o A246920 \\ Returns the number of cevians of an equilateral triangle of side n.
%o A246920 count(n) = {
%o A246920   s=[];
%o A246920   n=12*n^2;
%o A246920   fordiv(n, f,
%o A246920     g=n\f;
%o A246920     if(f<=g && (f+g)%2==0,
%o A246920       x=(f+g)\2;
%o A246920       if(x%4==0,
%o A246920         s=concat(s, x\4)
%o A246920       )
%o A246920     )
%o A246920   );
%o A246920   Colrev(s)~
%o A246920 }
%o A246920 vector(100, n, #count(n)-1)
%Y A246920 Cf. A229839, A246918, A246919.
%K A246920 nonn
%O A246920 1,5
%A A246920 _Colin Barker_, Sep 07 2014