A086243 - OEIS

A086243

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).

2, 14, 68, 604, 4312

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OFFSET

1,1

COMMENTS

A set of matrices closed under exponentiation.

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

LINKS

Table of n, a(n) for n=1..5.

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[%]

CROSSREFS

Cf. A072110.

Sequence in context: A084132 A271235 A084770 * A375874 A258138 A206947

Adjacent sequences: A086240 A086241 A086242 * A086244 A086245 A086246

KEYWORD

hard,nonn

AUTHOR

Wouter Meeussen, Aug 28 2003

STATUS

approved