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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

%I #19 Dec 10 2016 19:35:57

%S 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 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 5,8,2,8,2,2,9,2,8,5,2,14,4,2,2,5,8,2

%N 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 A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).

%C A nontrivial cevian is one that does not coincide with a side of the triangle.

%C 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 Colin Barker, <a href="/A246920/b246920.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Cevian">Cevian</a>

%e a(15) = 5 because cevians of an equilateral triangle of side 15 have length 13, 21, 35, 57 or 169.

%o (PARI)

%o \\ Returns the number of cevians of an equilateral triangle of side n.

%o count(n) = {

%o s=[];

%o n=12*n^2;

%o fordiv(n, f,

%o g=n\f;

%o if(f<=g && (f+g)%2==0,

%o x=(f+g)\2;

%o if(x%4==0,

%o s=concat(s, x\4)

%o )

%o )

%o );

%o Colrev(s)~

%o }

%o vector(100, n, #count(n)-1)

%Y Cf. A229839, A246918, A246919.

%K nonn

%O 1,5

%A _Colin Barker_, Sep 07 2014

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