A215723 -id:A215723 - cp's OEIS frontend

A215897 a(n) = A215723(n) / 2^(n-1).

1, 0, 1, 2, 3, 4, 8, 18, 27, 44, 267, 1024, 3645, 6144, 23859, 50176, 187377, 531468, 3302697, 10616832, 39337984, 102546588, 568833245, 3073593600, 8721488875, 32998447572, 164855413835, 572108938470, 2490252810073, 10831449635712, 68045615234375, 282773291271138, 1592413932070703, 5234078743146888

Offset: 1

Joerg Arndt, Aug 26 2012

A215723(n) is divisible by 2^(n-1), indeed the determinant of any n X n sign matrix is divisible by 2^(n-1). Proof: subtract the first row from other rows, the result is all rows except for the first are divisible by 2, hence by using expansion by minors proof follows. (Warren D. Smith on the math-fun mailing list, Aug 18 2012)

Richard P. Brent, Table of n, a(n) for n = 1..52
Richard P. Brent and Adam B. Yedidia, Computation of maximal determinants of binary circulant matrices, arXiv:1801.00399 [math.CO], 2018.
R. P. Brent and A. Yedidia, Computation of maximal determinants of binary circulant matrices, Journal of Integer Sequences, 21 (2018), article 18.5.6.
Index entries for sequences related to maximal determinants

Cf. A215723 (Maximum determinant of an n X n circulant (1,-1)-matrix).

a(n) = A215723(n) / 2^(n-1).

a(23)-a(28) (as calculated by Warren Smith) from W. Edwin Clark, Sep 02 2012

a(29) onward from Richard P. Brent, Jan 02 2018

A086432 Maximum of |det(A)| where A is an n X n circulant (0,1) matrix over the integers.

Original entry on oeis.org

1, 1, 2, 3, 4, 9, 32, 45, 95, 275, 1458, 2240, 6561, 19952, 131072, 214245, 755829, 2994003, 19531250, 37579575, 134534444, 577397064, 4353564672, 10757577600, 31495183733, 154611524732, 738139162166, 3124126889325, 11937232425585, 65455857159975

Offset: 1

Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 08 2003

Richard P. Brent, Table of n, a(n) for n = 1..53 (terms 1 to 37 from Hiroaki Yamanouchi)
Richard P. Brent and Adam B. Yedidia, Computation of maximal determinants of binary circulant matrices, arXiv:1801.00399 [math.CO], 2018.
R. P. Brent and A. Yedidia, Computation of maximal determinants of binary circulant matrices, Journal of Integer Sequences, 21 (2018), article 18.5.6.
Index entries for sequences related to maximal determinants

Cf. A086323.

Cf. A215723 (same for circulant (+1,-1) matrices), A215724 (same for (1,-1)-Toeplitz matrices).

Do[m=0;j=i-1;n=k=2^j; Do[l=IntegerDigits[k,2]; m=Max[m,Det[NestList[RotateRight,l,j]]]; k++,{n}]; Print[m], {i,30}] (* Hans Havermann, Dec 05 2012 *)

More terms from Vladeta Jovovic, Sep 09 2003
a(19)-a(22) from Joerg Arndt, Aug 25 2012
a(23)-a(30) from Hans Havermann, Dec 05 2012

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

Original entry on oeis.org

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

Offset: 1

W. Edwin Clark, Aug 22 2012

			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

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

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

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

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:

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

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

cp's OEIS Frontend

A215897 a(n) = A215723(n) / 2^(n-1).

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

Extensions

A086432 Maximum of |det(A)| where A is an n X n circulant (0,1) matrix over the integers.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

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

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Maple

Extensions