A174686 Number of equivalence classes of 3 X 3 matrices filled with n colors so that no two rotations are identical.

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

Author

Srikanth K S, Mar 27 2010

Keywords

• nonn

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.

Programs

PARI

a(n) = (n^9 - n^5)/4 \\ Michel Marcus, Mar 04 2013

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.

Extensions

More terms from Michel Marcus, Mar 04 2013