

A260417


Number of triplecrossings of diagonals in the regular 2ngon.


2



0, 1, 12, 30, 128, 147, 264, 1056, 600, 825, 2380, 1482, 1932, 9635, 3024, 3672, 8484, 5301, 6300, 19474, 8580, 9867, 20744, 12900, 14664, 30141, 18564, 20706, 62200, 25575, 28320, 54956, 34272, 37485, 62868, 44622, 48564, 86359, 57000, 61500, 117068, 71337
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,3


COMMENTS

Same as (total number of triangles visible in convex 2ngon with all diagonals drawn in general position)  (total number of triangles visible in regular 2ngon with all diagonals drawn).
Number of triplecrossings of diagonals in the regular 2n+1gon is 0.
See Sillke 1998 (where a(n) is called "T(2n)") for explanations and extensive annotated references.
See A005732 and A006600 for more comments, references, links, formulas, examples, programs, and lists from which to compute a(n) = A005732(2n)  A006600(2n) up to n = 500.


LINKS

Table of n, a(n) for n=2..43.
T. Sillke, Number of triangles for a convex ngon, 1998.


FORMULA

a(n) = A005732(2n)  A006600(2n).


EXAMPLE

With only 2 diagonals in a 4gon, there can be no triplecrossings, so a(2) = 0.


CROSSREFS

Sequences related to chords in a circle: A001006, A054726, A006533, A006561, A006600, A007569, A007678. See also entries for chord diagrams in Index file.
Sequence in context: A175157 A286659 A320483 * A117313 A080563 A221520
Adjacent sequences: A260414 A260415 A260416 * A260418 A260419 A260420


KEYWORD

nonn


AUTHOR

Jonathan Sondow, Jul 25 2015


STATUS

approved



