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A174686
Number of equivalence classes of 3 X 3 matrices filled with n colors so that no two rotations are identical.
0
120, 4860, 65280, 487500, 2517480, 10084200, 33546240, 96840360, 249975000, 589446660, 1289882880, 2651032020, 5165127240, 9610650000, 17179607040, 29646614160, 49589350200, 80671305420, 127999200000, 198568990620, 301816016040, 450286556280, 660449894400
OFFSET
2,1
COMMENTS
Each class contains a set of 4 matrices so that all of them can be obtained by successive rotation but no two are identical.
FORMULA
a(n) = (n^9 - n^(floor(9/2) + 1))/4. More generally for any m X m matrix f(n,m) = (n^(m^2) - n^(m^2/2))/4 if m is even, and f(n,m) = (n^(m^2) - n^(floor(m^2/2)+1))/4 if m is odd.
PROG
(PARI) a(n) = (n^9 - n^5)/4 \\ Michel Marcus, Mar 04 2013
CROSSREFS
Sequence in context: A111155 A283344 A223754 * A140907 A072419 A246193
KEYWORD
nonn
AUTHOR
Srikanth K S, Mar 27 2010
EXTENSIONS
More terms from Michel Marcus, Mar 04 2013
STATUS
approved