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URL: https://oeis.org/A060782

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A060782
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.
0
14, 3, 46, 7, 78, 11
OFFSET
1,1
COMMENTS
a(n) is also the degree of C(-n).
LINKS
A. P. Hatzipolakis, F. van Lamoen, B. Wolk and Paul Yiu, Concurrency of four Euler lines, Forum Geometricorum 1 (2001) 59 - 68.
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.
EXAMPLE
C(2) is a cubic curve, the well-known Neuberg cubic of a triangle, so a(2)=3.
CROSSREFS
Sequence in context: A040190 A317314 A163647 * A182431 A182440 A040187
KEYWORD
nonn,more
AUTHOR
Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Apr 28 2001
EXTENSIONS
Better description from Floor van Lamoen, Jul 10 2001
a(6) from Sean A. Irvine, Jan 01 2023
STATUS
approved