This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A215723 #60 Jul 23 2025 17:23:59
%S A215723 1,0,4,16,48,128,512,2304,6912,22528,273408,2097152,14929920,50331648,
%T A215723 390905856,1644167168,12279939072,69660573696,865782202368,
%U A215723 5566277615616,41248865910784,215055782117376,2385859554836480,25783171861708800,146322302697472000,1107244165160239104,11063259546716733440,76787161889935196160
%N A215723 Maximum determinant of an n X n circulant (1,-1)-matrix.
%C A215723 a(n) is divisible by 2^(n-1), see A215897. [_Joerg Arndt_, Aug 26 2012]
%D A215723 Warren D. Smith, Posting to the Math Fun Mailing List August 18, 2012.
%H A215723 Amiram Eldar, <a href="/A215723/b215723.txt">Table of n, a(n) for n = 1..52</a> (calculated from the b-file at A215897)
%H A215723 Richard P. Brent and Adam B. Yedidia, <a href="http://arxiv.org/abs/1801.00399">Computation of maximal determinants of binary circulant matrices</a>, arXiv:1801.00399 [math.CO], 2018.
%H A215723 John Holbrook, Nathaniel Johnston, and Jean-Pierre Schoch, <a href="https://arxiv.org/abs/2206.02863">Real Schur norms and Hadamard matrices</a>, arXiv:2206.02863 [math.CO], 2022.
%H A215723 N. J. A. Sloane, <a href="/A215723/a215723.txt">Table from Warren Smith's Aug 31 2012 posting to Math Fun Mailing List</a> [Gives n, a(n) and first row of matrix for n <= 28. I do not know how rigorous these results are.]
%H A215723 Wikipedia, <a href="http://en.wikipedia.org/wiki/Circulant_matrix">Circulant matrix</a>.
%H A215723 <a href="/index/De#determinants">Index entries for sequences related to maximal determinants</a>.
%p A215723 a:=proc(n)
%p A215723 local T, b, U, M,d,r;
%p A215723 T:= combinat:-cartprod([seq({-1, 1}, j = 1 .. n)]);
%p A215723 b:= 0;
%p A215723 while not T[finished] do
%p A215723 U := T[nextvalue]();
%p A215723 M := Matrix(n, shape = Circulant[U]);
%p A215723 d:= LinearAlgebra:-Determinant(M):
%p A215723 if d > b then b := d; end if;
%p A215723 end do;
%p A215723 return b;
%p A215723 end proc:
%o A215723 (PARI) a(n)={my(m=0); for(p=n>1, 2^(n-1)-1, m=max(m, matdet(matrix(n, n, i, j, 1-2*bittest(p, (i-j)%n))))); m} /* For illustrative purpose only: becomes slow for n>15 */ /* _M. F. Hasler_, Aug 25 2012 */
%Y A215723 Cf. A003433, A086432 (same for circulant (0,1) matrices), A215724 (same for (1,-1)-Toeplitz matrices).
%Y A215723 Cf. A215897 ( =a(n)/2^(n-1) ).
%K A215723 nonn,hard
%O A215723 1,3
%A A215723 _W. Edwin Clark_, Aug 22 2012
%E A215723 a(16)-a(22) from _Joerg Arndt_, Aug 25 2012
%E A215723 a(23)-a(28) (as calculated by Warren Smith) from _W. Edwin Clark_, Sep 02 2012