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

2,3

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.

Links

Table of n, a(n) for n=2..43.

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

Formula

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

Example

With only 2 diagonals in a 4-gon, there can be no triple-crossings, 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: A320483 A361468 A361467 * A117313 A080563 A221520

Adjacent sequences: A260414 A260415 A260416 * A260418 A260419 A260420

Keyword

nonn

Author

Jonathan Sondow, Jul 25 2015

Status

approved