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Number of invertible (-1,0,1) n X n matrices having (Tij=-Tji; i<j) such that all T^k (k= 1..12) are also (-1,0,1) invertible matrices having (Tij=-Tji; i<j).
0

%I #4 Mar 30 2012 18:37:43

%S 2,14,68,604,4312

%N Number of invertible (-1,0,1) n X n matrices having (Tij=-Tji; i<j) such that all T^k (k= 1..12) are also (-1,0,1) invertible matrices having (Tij=-Tji; i<j).

%C A set of matrices closed under exponentiation.

%C The powers T^k are themselves all members of the set that is counted.

%t (* trimatsig[ ] : see A072110 *) n=3; it=triamatsig/@(-1+IntegerDigits[Range[0, -1+3^(n(n+1)/2)], 3, n(n+1)/2]); result[n]=Cases[it, (q_?MatrixQ)/; Det[q]=!=0 && And@@Table[Union[Flatten[{(temp=MatrixPower[q, k]), {-1, 0, 1}}]]==={-1, 0, 1} && ((1-IdentityMatrix[n])temp===-Transpose[(1-IdentityMatrix[n])temp]), {k, 12}]]; Length[%]

%Y Cf. A072110.

%K hard,nonn

%O 1,1

%A _Wouter Meeussen_, Aug 28 2003