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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

%I #11 Mar 04 2013 10:48:25

%S 120,4860,65280,487500,2517480,10084200,33546240,96840360,249975000,

%T 589446660,1289882880,2651032020,5165127240,9610650000,17179607040,

%U 29646614160,49589350200,80671305420,127999200000,198568990620,301816016040,450286556280,660449894400

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

%C Each class contains a set of 4 matrices so that all of them can be obtained by successive rotation but no two are identical.

%F 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.

%o (PARI) a(n) = (n^9 - n^5)/4 \\ _Michel Marcus_, Mar 04 2013

%K nonn

%O 2,1

%A _Srikanth K S_, Mar 27 2010

%E More terms from _Michel Marcus_, Mar 04 2013

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Last modified February 23 03:03 EST 2024. Contains 370266 sequences. (Running on oeis4.)