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%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
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