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A215723
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Maximum determinant of an n X n circulant (1,-1)-matrix.
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3
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1, 0, 4, 16, 48, 128, 512, 2304, 6912, 22528, 273408, 2097152, 14929920, 50331648, 390905856, 1644167168, 12279939072, 69660573696, 865782202368, 5566277615616, 41248865910784, 215055782117376, 2385859554836480, 25783171861708800, 146322302697472000, 1107244165160239104, 11063259546716733440, 76787161889935196160
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OFFSET
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1,3
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COMMENTS
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REFERENCES
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Warren D. Smith, Posting to the Math Fun Mailing List August 18, 2012.
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LINKS
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MAPLE
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a:=proc(n)
local T, b, U, M, d, r;
T:= combinat:-cartprod([seq({-1, 1}, j = 1 .. n)]);
b:= 0;
while not T[finished] do
U := T[nextvalue]();
M := Matrix(n, shape = Circulant[U]);
d:= LinearAlgebra:-Determinant(M):
if d > b then b := d; end if;
end do;
return b;
end proc:
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PROG
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(PARI) a(n)={my(m=0); for(p=n>1, 2^(n-1)-1, m=max(m, matdet(matrix(n, n, i, j, 1-2*bittest(p, (i-j)%n))))); m} /* For illustrative purpose only: becomes slow for n>15 */ /* M. F. Hasler, Aug 25 2012 */
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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EXTENSIONS
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a(23)-a(28) (as calculated by Warren Smith) from W. Edwin Clark, Sep 02 2012
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STATUS
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approved
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