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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 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

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