login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000545 Number of ways of n-coloring a dodecahedron. 4
1, 96, 9099, 280832, 4073375, 36292320, 230719293, 1145393152, 4707296613, 16666924000, 52307593239, 148602435840, 388302646355, 944900450144, 2162441849625, 4691253854208, 9710376716137, 19280531603808, 36888593841475, 68266682784000, 122597146773927 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

More explicitly, a(n) is the number of colorings with at most n colors of the faces of a regular dodecahedron, inequivalent under the action of the rotation group of the dodecahedron. It is also the number of inequivalent colorings of the vertices of a regular icosahedron using at most n colors. - José H. Nieto S., Jan 19 2012

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Polyhedron Coloring

FORMULA

G.f.: x*((1+x)*(1+x*(82+x*(7847+x*(161900+x*(943640+x*(1764740+x*(943640+x*(161900+x*(7847+x*(82+x)))))))))))/(1-x)^13. - Harvey P. Dale, Apr 25 2011

a(n)=C(n,1)+94C(n,2)+8814C(n,3)+245008C(n,4)+2759250C(n,5)+15884004C(n,6)+52701264C(n,7)+106866144C(n,8)+134719200C(n,9)+103118400C(n,10)+43908480C(n,11)+7983360C(n,12). Each term indicates the number of ways to use n colors to color the dodecahedron faces (icosahedron vertices) with exactly 1, 2, 3, ..., 10, 11, or 12 colors.

MAPLE

(1/60)*n^12+(1/4)*n^6+(11/15)*n^4;

MATHEMATICA

Table[n^12/60+n^6/4+11 n^4/15, {n, 20}] (* or *) CoefficientList[Series[ -(((1+x) (1+x (82+x (7847+x (161900+x (943640+x (1764740+x (943640+x (161900+x (7847+x (82+x)))))))))))/(x-1)^13), {x, 0, 20}], x] (* Harvey P. Dale, Apr 25 2011 *)

CROSSREFS

Cf. A006550.

Sequence in context: A093248 A299856 A270603 * A189909 A189903 A189159

Adjacent sequences:  A000542 A000543 A000544 * A000546 A000547 A000548

KEYWORD

nonn,easy

AUTHOR

Clint. C. Williams (Clintwill(AT)aol.com)

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 19 12:57 EDT 2019. Contains 327198 sequences. (Running on oeis4.)