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

Author

W. Edwin Clark, Aug 22 2012

Keywords

• nonn
• hard
• more

Examples

			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
		

References

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

Links

• Lucas A. Brown, A215724.py.
• Wikipedia, Toeplitz Matrix
• Index entries for sequences related to maximal determinants

Crossrefs

Cf. A086432 (same for circulant (0,1) matrices), A215723 (same for circulant (+1,-1) matrices).

Programs

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:

Extensions

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

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