|
| |
|
|
A320604
|
|
Chromatic number of the n-polygon diagonal intersection graph.
|
|
0
|
|
|
|
4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Extended to a(1)-a(2) using the formula/recurrence.
|
|
|
LINKS
|
Table of n, a(n) for n=1..92.
Eric Weisstein's World of Mathematics, Chromatic Number
Eric Weisstein's World of Mathematics, Polygon Diagonal Intersection Graph
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 1).
|
|
|
FORMULA
|
a(n) = (10 - (-1)^n + cos(n*Pi/3) - cos(2*n*Pi/3))/3.
a(n) = a(n-6).
G.f.: -x^3*(3 + 3*x + 4*x^2 + 3*x^3 + 4*x^4 + 3*x^5)/((-1 + x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2)).
E.g.f.: (1/6)*exp(-x)*(-2-18*exp(x)+20*exp(2*x)+exp((1+(-1)^(1/3))*x)-exp((1+(-1)^(2/3))*x)-exp(x-(-1)^(1/3)*x)+exp(x-(-1)^(2/3)*x)). - Stefano Spezia, Oct 17 2018
|
|
|
MATHEMATICA
|
Table[(10 - (-1)^n + Cos[n Pi/3] - Cos[2 n Pi/3])/3, {n, 20}]
Table[Piecewise[{{4, Mod[n, 6] == 1 || Mod[n, 6] == 5}}, 3], {n, 20}]
LinearRecurrence[{0, 0, 0, 0, 0, 1}, {4, 3, 3, 3, 4, 3}, 20]
CoefficientList[Series[-((3 + 3 x + 4 x^2 + 3 x^3 + 4 x^4 + 3 x^5)/((-1 + x) (1 + x) (1 - x + x^2) (1 + x + x^2))), {x, 0, 20}], x]
Simplify[CoefficientList[Series[1/6 E^-x (-2 - 18 E^x + 20 E^(2 x) + E^((1 + (-1)^(1/3)) x) - E^((1 + (-1)^(2/3)) x) - E^(x - (-1)^(1/3) x) + E^(x - (-1)^(2/3) x))/x, {x, 0, 50}], x]*Table[(k+1)!, {k, 0, 50}]] (* Stefano Spezia, Oct 17 2018 *)
|
|
|
CROSSREFS
|
Sequence in context: A085415 A187470 A059124 * A282445 A281705 A026858
Adjacent sequences: A320601 A320602 A320603 * A320605 A320606 A320607
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Eric W. Weisstein, Oct 17 2018
|
|
|
STATUS
|
approved
|
| |
|
|
