|
| |
|
|
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
M. F. Hasler, Interactive illustration of A006561(n) & A006533(n); colored version for n=6 and for n=8.
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,...
Sequences formed by drawing all diagonals in regular polygon
|
|
|
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
|
| |
|
|
