The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A359009 Irregular table read by rows: T(n,k) is the number of k-gons formed, k>=2, when every pair of n points, placed at the vertices of a regular n-gon, are connected by a circle and where the points lie at the ends of the circle's diameter. 11
 1, 0, 7, 8, 4, 0, 40, 20, 6, 6, 72, 6, 0, 0, 0, 0, 0, 0, 0, 1, 0, 133, 98, 42, 7, 1, 16, 184, 56, 0, 8, 0, 342, 306, 99, 54, 0, 0, 1, 10, 510, 220, 60, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 693, 858, 231, 88, 11, 11, 0, 0, 1, 24, 924, 612, 120, 60, 0, 1469, 1560, 455, 299, 13, 0, 0, 13, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS Conjectures: for odd values of n all vertices are simple, other than those defining the diameters of the circles. For n > 2 and (n-2) mod 4 = 0, T(n,2) = n. For n mod 4 = 0, T(n,2) = k*n, k>=2. For odd n, T(n,2) = 0. See A358782 for more images of the k-gons. The author thanks Zach Shannon some of whose code was used in the generation of this sequence. LINKS Table of n, a(n) for n=2..86. Scott R. Shannon, Image for n = 13. Scott R. Shannon, Image for n = 21. FORMULA Sum of row n = A358782(n). EXAMPLE The table begins: 1; 0, 7; 8, 4; 0, 40, 20, 6; 6, 72, 6, 0, 0, 0, 0, 0, 0, 0, 1; 0, 133, 98, 42, 7, 1; 16, 184, 56, 0, 8; 0, 342, 306, 99, 54, 0, 0, 1; 10, 510, 220, 60, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; 0, 693, 858, 231, 88, 11, 11, 0, 0, 1; 24, 924, 612, 120, 60; 0, 1469, 1560, 455, 299, 13, 0, 0, 13, 0, 0, 1; 14, 1806, 1428, 350, 98, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \\ 0, 0, 0, 1; 0, 2550, 2910, 870, 405, 75, 60, 0, 0, 0, 0, 0, 0, 1; 32, 3280, 2000, 768, 352, 0, 16; 0, 4301, 4862, 1734, 680, 102, 34, 0, 17, 0, 17, 0, 0, 0, 0, 1; 18, 4878, 4482, 1332, 324, 54, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \\ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; 0, 6517, 7847, 2565, 1045, 190, 133, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; 80, 7340, 7040, 1920, 700, 0, 80; 0, 9723, 11487, 4515, 1491, 210, 168, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; . . CROSSREFS Cf. A358782 (regions), A358746 (vertices), A358783 (edges), A331451, A344938. Sequence in context: A193010 A079082 A091683 * A092157 A220351 A220863 Adjacent sequences: A359006 A359007 A359008 * A359010 A359011 A359012 KEYWORD nonn,tabf AUTHOR Scott R. Shannon, Dec 12 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 10 04:11 EDT 2024. Contains 375773 sequences. (Running on oeis4.)