

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
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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) = (n2)^2*(n1)*n^2*(n+5)/24.
G.f.: 3*x^3*(210*x+x^2+x^3)/(x1)^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



