A086243 Number of invertible (-1,0,1) n X n matrices having (Tij=-Tji; i

2, 14, 68, 604, 4312

Offset: 1

Author

Wouter Meeussen, Aug 28 2003

Keywords

• hard
• nonn

Comments

A set of matrices closed under exponentiation.

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

Crossrefs

Cf. A072110.

Programs

Mathematica

(* 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[%]