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 A344866 Number of polygons formed when every pair of vertices of a regular (2n-1)-gon are joined by an infinite line. 9
 0, 1, 16, 99, 352, 925, 2016, 3871, 6784, 11097, 17200, 25531, 36576, 50869, 68992, 91575, 119296, 152881, 193104, 240787, 296800, 362061, 437536, 524239, 623232, 735625, 862576, 1005291, 1165024, 1343077, 1540800, 1759591, 2000896, 2266209, 2557072, 2875075, 3221856, 3599101, 4008544, 4451967 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This is the odd-indexed subsequence of A344857. See A344857 for images of the polygons. LINKS Table of n, a(n) for n=1..40. John Elias, Illustration of initial terms: Cubic Vertex Fractal J. F. Rigby, Multiple intersections of diagonals of regular polygons, and related topics, Geom. Dedicata 9 (1980), 207-238. Alexander Sidorenko, Explicit Formulas for Odd-Indexed Terms in A344899, A146212, and A344857. Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = 2*n^4 - 11*n^3 + 23*n^2 - 21*n + 7. G.f.: x^2*(1 + 11*x + 29*x^2 + 7*x^3)/(1 - x)^5. - Stefano Spezia, Jun 04 2021 EXAMPLE a(3) = 16 as the five connected vertices form eleven polygons inside the regular pentagon while also forming five triangles outside the pentagon, giving sixteen polygons in total. PROG (Python) def A344866(n): return n*(n*(n*(2*n - 11) + 23) - 21) + 7 # Chai Wah Wu, Sep 12 2021 CROSSREFS Cf. A344857 (number for even and odd n), A344311, A344938, A007678, A341735 (number inside the n-gon), A344899 (number of edges). See also A347320. Sequence in context: A214612 A283545 A297684 * A322722 A014762 A045784 Adjacent sequences: A344863 A344864 A344865 * A344867 A344868 A344869 KEYWORD nonn,easy AUTHOR Scott R. Shannon, Jun 01 2021 EXTENSIONS Edited by N. J. A. Sloane, Sep 12 2021 STATUS approved

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Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)