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

1, 2, 4, 16, 48, 160, 576, 2560, 12288, 73728, 327680, 2097152, 14929920, 68853760, 390905856, 2363752448

Offset

1,2

References

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

Links

Table of n, a(n) for n=1..16.

Lucas A. Brown, A215724.py.

Wikipedia, Toeplitz Matrix

Index entries for sequences related to maximal determinants

Example

a(2) = 2:
    1  1
   -1  1
a(3) = 4:
    1  1  1
   -1  1  1
    1 -1  1
a(6) = 160
    1 -1  1  1  1  1
   -1  1 -1  1  1  1
   -1 -1  1 -1  1  1
   -1 -1 -1  1 -1  1
    1 -1 -1 -1  1 -1
    1  1 -1 -1 -1  1

Maple

a:=proc(n)
local T, b, U, M, d, r;
T:= combinat:-cartprod([seq({-1, 1}, j = 1..2*n-1)]);
b:= 0;
while not T[finished] do
   U := T[nextvalue]();
   M := LinearAlgebra:-ToeplitzMatrix(U, n);
   d:= abs(LinearAlgebra:-Determinant(M)):
   if d > b then b := d; end if;
end do;
return b;
end proc:

Crossrefs

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

Sequence in context: A103435 A119000 A034917 * A003433 A153951 A248748

Adjacent sequences: A215721 A215722 A215723 * A215725 A215726 A215727

Keyword

nonn,hard,more

Author

W. Edwin Clark, Aug 22 2012

Extensions

a(15) from Lucas A. Brown, Sep 06 2022

a(16) from Lucas A. Brown, Nov 03 2022

Status

approved