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A282817 Number of inequivalent ways to color the faces of a cube using at most n colors so that no color appears more than twice. 2
0, 0, 0, 6, 72, 375, 1320, 3675, 8736, 18522, 36000, 65340, 112200, 184041, 290472, 443625, 658560, 953700, 1351296, 1877922, 2565000, 3449355, 4573800, 5987751, 7747872, 9918750, 12573600, 15795000, 19675656, 24319197, 29841000, 36369045, 44044800, 53024136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Also the number of inequivalent ways to color the corners of an octahedron using at most n colors so that no color appears more than twice.

LINKS

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

a(n) = (n-2)^2*(n-1)*n^2*(n+5)/24.

G.f.: 3*x^3*(-2-10*x+x^2+x^3)/(x-1)^7 . - R. J. Mathar, Feb 23 2017

EXAMPLE

For n=3 we get a(3)=6 ways to color the faces of a cube with three colors so that no color appears more than twice.

MATHEMATICA

Table[(3 n (n - 1) (n - 2)^2 + 6 n (n - 1) (n - 2) + n (n - 1) (n - 2) (n - 3) (n - 4) (n - 5) + 15 n (n - 1) (n - 2) (n - 3) (n - 4) + 45 n (n - 1) (n - 2) (n - 3) + 15 n (n - 1) (n - 2))/24, {n, 0, 16}]

CROSSREFS

Cf. A249460, A282816. A047780 (face colorings without restriction).

Sequence in context: A250071 A192990 A276244 * A274955 A177468 A052791

Adjacent sequences:  A282814 A282815 A282816 * A282818 A282819 A282820

KEYWORD

nonn,easy

AUTHOR

David Nacin, Feb 21 2017

STATUS

approved

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)