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A056989
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Number of nonsingular n X n (-1,0,1)-matrices (over the reals).
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6
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OFFSET
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0,2
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COMMENTS
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It would be nice to have an estimate for the asymptotic rate of growth.
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 2: [1], [ -1].
a(2) = 48: There are 8 choices for the first column, u (say) and then the 2nd column can be anything except 0, u, -u, so 6 choices, giving a total of 8*6 = 48.
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MATHEMATICA
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(* A brute force solution up to n = 4 *) a[n_] := a[n] = (m = Array[x, {n, n}]; cnt = 0; iter = {#, -1, 1}& /@ Flatten[m]; Do[ If[ Det[m] != 0, cnt++], Evaluate[ Sequence @@ iter]]; cnt); Table[ Print[a[n]]; a[n], {n, 1, 4}] (* Jean-François Alcover, Oct 11 2012 *)
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CROSSREFS
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KEYWORD
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nonn,nice,more
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AUTHOR
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EXTENSIONS
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a(4) from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 27 2000
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STATUS
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approved
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