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A036403
Number of equilateral triangles whose vertices (whether connected by lines or not) lie at intersection points resulting from drawing lines connecting every pair of vertices of a regular 3n-gon (and extending beyond the polygon).
1
1, 126, 3927, 33156, 97115, 641916, 537607, 4222280, 1744695, 20962830, 4003241, 42626916
OFFSET
1,2
COMMENTS
Given a regular 3n-gon, draw a line, extending beyond the polygon, through every pair of vertices; a(n) is the number of distinct equilateral triangles whose vertices lie at three of the resulting intersection points (whether the three points are connected by lines or not).
REFERENCES
Computed by Ilan Mayer (ilan(AT)isgtec.com).
EXAMPLE
Drawing lines connecting every pair of vertices on a regular hexagon (6-gon) and extending those lines beyond the polygon results in 37 distinct intersection points. Of the 37 * 36 * 35 / 3! = 7770 sets of 3 of those intersection points that could be selected, there are 126 sets of 3 intersection points such that, if the 3 points were connected by line segments, the resulting triangle would be equilateral, so a(2)=126.
CROSSREFS
Cf. A006600.
Sequence in context: A285921 A086024 A285857 * A286976 A186816 A292882
KEYWORD
nonn,nice,more
AUTHOR
Antreas P. Hatzipolakis (xpolakis(AT)hol.gr)
EXTENSIONS
Added a(5) through a(8), corrected definition and comment and provided example, after receiving clarification Oct 22 2008 from Ilan Mayer (who had originally computed the sequence) regarding its definition. - Jon E. Schoenfield, Oct 23 2008
a(9)-a(12) from Jon E. Schoenfield, Oct 26 2008
STATUS
approved