A260417 Number of triple-crossings of diagonals in the regular 2n-gon.

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

Offset: 2

Author

Jonathan Sondow, Jul 25 2015

Keywords

• nonn

Comments

Same as (total number of triangles visible in convex 2n-gon with all diagonals drawn in general position) - (total number of triangles visible in regular 2n-gon with all diagonals drawn).

Number of triple-crossings of diagonals in the regular 2n+1-gon 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.

Examples

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

Links

• T. Sillke, Number of triangles for a convex n-gon, 1998.

Crossrefs

Sequences related to chords in a circle: A001006, A054726, A006533, A006561, A006600, A007569, A007678. See also entries for chord diagrams in Index file.

Formula

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