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 A260417 Number of triple-crossings of diagonals in the regular 2n-gon. 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 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 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: A175157 A286659 A320483 * A117313 A080563 A221520 Adjacent sequences:  A260414 A260415 A260416 * A260418 A260419 A260420 KEYWORD nonn AUTHOR Jonathan Sondow, Jul 25 2015 STATUS approved

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Last modified March 30 08:26 EDT 2020. Contains 333119 sequences. (Running on oeis4.)