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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

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

Sequences formed by drawing all diagonals in regular polygon

FORMULA

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

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Last modified April 29 11:38 EDT 2017. Contains 285604 sequences.