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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). 0
2, 14, 68, 604, 4312 (list; graph; refs; listen; history; text; internal format)
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
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 * A258138 A206947 A203241
KEYWORD
hard,nonn
AUTHOR
Wouter Meeussen, Aug 28 2003
STATUS
approved

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Last modified March 28 04:05 EDT 2024. Contains 371235 sequences. (Running on oeis4.)