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A215724 Maximum absolute value of determinant of n X n (1,-1)-Toeplitz matrix. 3

%I

%S 1,2,4,16,48,160,576,2560,12288,73728,327680,2097152,14929920,68853760

%N Maximum absolute value of determinant of n X n (1,-1)-Toeplitz matrix.

%D Warren D. Smith, Posting to the Math Fun Mailing List, August 18, 2012.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>

%H <a href="/index/De#determinants">Index entries for sequences related to maximal determinants</a>

%p a:=proc(n)

%p local T, b, U, M,d,r;

%p T:= combinat:-cartprod([seq({-1, 1}, j = 1..2*n-1)]);

%p b:= 0;

%p while not T[finished] do

%p U := T[nextvalue]();

%p M := LinearAlgebra:-ToeplitzMatrix(U,n);

%p d:= abs(LinearAlgebra:-Determinant(M)):

%p if d > b then b := d; end if;

%p end do;

%p return b;

%p end proc:

%Y Cf. A086432 (same for circulant (0,1) matrices), A215724 (same for circulant (+1,-1) matrices).

%K nonn,hard,more

%O 1,2

%A _W. Edwin Clark_, Aug 22 2012

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Last modified June 6 03:48 EDT 2020. Contains 334858 sequences. (Running on oeis4.)