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

2,1

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.

Links

Table of n, a(n) for n=2..24.

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

Adjacent sequences: A174683 A174684 A174685 * A174687 A174688 A174689

Keyword

nonn

Author

Srikanth K S, Mar 27 2010

Extensions

More terms from Michel Marcus, Mar 04 2013

Status

approved