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A060782
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Degree of the curve C(n) relative to a triangle ABC with side lengths a, b and c, given by (x^n- b^n)(y^n-c^n)(z^n-a^n)=(x^n-c^n)(y^n-a^n)(z^n-b^n) where x, y and z denote the distances from the variable point to vertices A, B and C respectively.
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OFFSET
| 1,1
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COMMENTS
| a(n) is also the degree of C(-n).
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LINKS
| A. P. Hatzipolakis, F. van Lamoen, B. Wolk and Paul Yiu, Concurrency of four Euler lines, Forum Geometricorum 1 (2001) 59 - 68.
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FORMULA
| It is known that a(n) = 2n-1 for n even; a(1) = 14; a(3) = 46; and it is conjectured that a(n) = 16n-2 for n odd.
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EXAMPLE
| C(2) is a cubic curve, the well-known Neuberg cubic of a triangle, so a(2)=3.
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CROSSREFS
| Sequence in context: A204159 A040190 A163647 * A040187 A164811 A018813
Adjacent sequences: A060779 A060780 A060781 * A060783 A060784 A060785
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KEYWORD
| nonn
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AUTHOR
| Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Apr 28 2001
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EXTENSIONS
| Better description from Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 10 2001
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