%I #27 Nov 03 2022 05:43:24
%S 1,2,4,16,48,160,576,2560,12288,73728,327680,2097152,14929920,
%T 68853760,390905856,2363752448
%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 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A215724.py">A215724.py</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%H <a href="/index/De#determinants">Index entries for sequences related to maximal determinants</a>
%e a(2) = 2:
%e 1 1
%e -1 1
%e a(3) = 4:
%e 1 1 1
%e -1 1 1
%e 1 -1 1
%e a(6) = 160
%e 1 -1 1 1 1 1
%e -1 1 -1 1 1 1
%e -1 -1 1 -1 1 1
%e -1 -1 -1 1 -1 1
%e 1 -1 -1 -1 1 -1
%e 1 1 -1 -1 -1 1
%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
%E a(15) from _Lucas A. Brown_, Sep 06 2022
%E a(16) from _Lucas A. Brown_, Nov 03 2022
|