rehash of thread 15/08/2003, with some news. OEIS?Anum=A072148 Sequence: 2,14,92,796,7672 Definitions: pseudoAntisymmetric : T(i,j)= -T(j,i) for j<i , so T = diagonal+Antisymmetric. (my definition, forgive..) powerlength: minimal p>0 so that T^p = Identity Consider the (-1,0,1)-matrices T with properties : Det[T] not zero (invertible), all powers T^k are also invertible (-1,0,1) matrices. Properties: powerlength of T divides 12, Det[t] is 1 or -1, T is pseudoAntisymmetric, the powers T^k need not be all pseudoAntisymmetric: for 4x4 matrices, all those with 8 non-zero elements have powerlength 4, and their powers 2 and 3 are not pseudoAntisymmetric; for the 5x5 matrices, all those with 9 non-zero elements have powerlength 4, and their powers 2 and 3 are not pseudoAntisymmetric; all those with 10 non-zero elements have powerlength 12, and their powers 2,3,6,7,10 and 11 are not pseudoAntisymmetric; There is a system in this madness, but this margin is too small... W. (I owe Marc LeBrun <mlb@fxpt.com> for help, partial insight & lots inspiration, thanx Marc) I put the 796 4-by4 and the 7672 5-by-5 on http://users.pandora.be/Wouter.Meeussen/pseudoAntisymmMatrixPowers_4.txt http://users.pandora.be/Wouter.Meeussen/pseudoAntisymmMatrixPowers_5.txt