This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A006533 Join n equal points around circle in all ways, count regions. (Formerly M1118) 13
 1, 2, 4, 8, 16, 30, 57, 88, 163, 230, 386, 456, 794, 966, 1471, 1712, 2517, 2484, 4048, 4520, 6196, 6842, 9109, 9048, 12951, 14014, 17902, 19208, 24158, 21510, 31931, 33888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES Jean Meeus, Wiskunde Post (Belgium), Vol. 10, 1972, pp. 62-63. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 Sascha Kurz, m-gons in regular n-gons J. Meeus & N. J. A. Sloane, Correspondence, 1974-1975 B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156. B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, SIAM J. on Discrete Mathematics, Vol. 11, No. 1, 135-156 (1998). B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, arXiv version, which has fewer typos than the SIAM version. B. Poonen and M. Rubinstein, Mathematica programs for these sequences M. Rubinstein, Drawings for n=4,5,6,... FORMULA Poonen and Rubinstein give an explicit formula for a(n). a(n)=A007678(n)+n. - T. D. Noe, Dec 23 2006 MATHEMATICA del[m_, n_]:=If[Mod[n, m]==0, 1, 0]; R[n_]:=(n^4-6n^3+23n^2-18n+24)/24 + del[2, n](-5n^3+42n^2-40n-48)/48 - del[4, n](3n/4) + del[6, n](-53n^2+310n)/12 + del[12, n](49n/2) + del[18, n]*32n + del[24, n]*19n - del[30, n]*36n - del[42, n]*50n - del[60, n]*190n - del[84, n]*78n - del[90, n]*48n - del[120, n]*78n - del[210, n]*48n; Table[R[n], {n, 1, 1000}] (* T. D. Noe, Dec 21 2006 *) 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: A164256 A164240 A164214 * A164188 A164186 A164187 Adjacent sequences:  A006530 A006531 A006532 * A006534 A006535 A006536 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane, Bjorn Poonen (poonen(AT)math.princeton.edu) STATUS approved

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

Last modified October 16 07:30 EDT 2019. Contains 328051 sequences. (Running on oeis4.)