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

%I A215724 #29 Aug 29 2024 16:41:57
%S A215724 1,2,4,16,48,160,576,2560,12288,73728,327680,2097152,14929920,
%T A215724 68853760,390905856,2363752448
%N A215724 Maximum absolute value of determinant of n X n (1,-1)-Toeplitz matrix.
%D A215724 Warren D. Smith, Posting to the Math Fun Mailing List, August 18, 2012.
%H A215724 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A215724.py">A215724.py</a>.
%H A215724 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%H A215724 <a href="/index/De#determinants">Index entries for sequences related to maximal determinants</a>
%e A215724 a(2) = 2:
%e A215724     1  1
%e A215724    -1  1
%e A215724 a(3) = 4:
%e A215724     1  1  1
%e A215724    -1  1  1
%e A215724     1 -1  1
%e A215724 a(6) = 160
%e A215724     1 -1  1  1  1  1
%e A215724    -1  1 -1  1  1  1
%e A215724    -1 -1  1 -1  1  1
%e A215724    -1 -1 -1  1 -1  1
%e A215724     1 -1 -1 -1  1 -1
%e A215724     1  1 -1 -1 -1  1
%p A215724 a:=proc(n)
%p A215724 local T, b, U, M,d,r;
%p A215724 T:= combinat:-cartprod([seq({-1, 1}, j = 1..2*n-1)]);
%p A215724 b:= 0;
%p A215724 while not T[finished] do
%p A215724    U := T[nextvalue]();
%p A215724    M := LinearAlgebra:-ToeplitzMatrix(U,n);
%p A215724    d:= abs(LinearAlgebra:-Determinant(M)):
%p A215724    if d > b then b := d; end if;
%p A215724 end do;
%p A215724 return b;
%p A215724 end proc:
%Y A215724 Cf. A086432 (same for circulant (0,1) matrices), A215723 (same for circulant (+1,-1) matrices).
%K A215724 nonn,hard,more
%O A215724 1,2
%A A215724 _W. Edwin Clark_, Aug 22 2012
%E A215724 a(15) from _Lucas A. Brown_, Sep 06 2022
%E A215724 a(16) from _Lucas A. Brown_, Nov 03 2022