|
|
A213222
|
|
Minimum number of distinct slopes formed by n noncollinear points in the plane.
|
|
3
|
|
|
3, 4, 4, 6, 6, 8, 8, 10, 10, 12, 12, 14, 14, 16, 16, 18, 18, 20, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 32, 32, 34, 34, 36, 36, 38, 38, 40, 40, 42, 42, 44, 44, 46, 46, 48, 48, 50, 50, 52, 52, 54, 54, 56, 56, 58, 58, 60, 60, 62, 62, 64, 64, 66, 66, 68, 68, 70, 70, 72, 72, 74, 74, 76, 76, 78, 78, 80, 80, 82, 82, 84
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
3,1
|
|
COMMENTS
|
Scott formulated the problem (on the basis of a similar problem of Erdős), gave bounds, and conjectured the formula which Unger later proved.
Also the edge chromatic number of the n-polygon diagonal intersection graph. - Eric W. Weisstein, Mar 23 2018
|
|
REFERENCES
|
Martin Aigner and Gunter M. Ziegler, Proofs from THE BOOK, Second Edition, Springer-Verlag, Berlin, 2000. Chapter 10.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2*floor(n/2) for n > 3.
G.f.: x^3*(3+x-3*x^2+x^3)/((1+x)*(1-x)^2). [Bruno Berselli, Mar 04 2013]
|
|
MAPLE
|
|
|
MATHEMATICA
|
CoefficientList[Series[(3 + x - 3 x^2 + x^3)/((1 + x) (1 - x)^2), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 29 2014 *)
|
|
PROG
|
(PARI) a(n)=if(n>3, n\2*2, 3)
|
|
CROSSREFS
|
Cf. A000217 (maximum number of slopes, with offset 1).
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|