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 A215723 Maximum determinant of an n X n circulant (1,-1)-matrix. 3
 1, 0, 4, 16, 48, 128, 512, 2304, 6912, 22528, 273408, 2097152, 14929920, 50331648, 390905856, 1644167168, 12279939072, 69660573696, 865782202368, 5566277615616, 41248865910784, 215055782117376, 2385859554836480, 25783171861708800, 146322302697472000, 1107244165160239104, 11063259546716733440, 76787161889935196160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) is divisible by 2^(n-1), see A215897. [Joerg Arndt, Aug 26 2012] REFERENCES Warren D. Smith, Posting to the Math Fun Mailing List August 18, 2012. LINKS Richard P. Brent and Adam B. Yedidia, Computation of maximal determinants of binary circulant matrices, arXiv:1801.00399 [math.CO], 2018. N. J. A. Sloane, Table from Warren Smith's Aug 31 2012 posting to Math Fun Mailing List [Gives n, a(n) and first row of matrix for n <= 28. I do not know how rigorous these results are.] Wikipedia, Circulant matrix MAPLE a:=proc(n) local T, b, U, M, d, r; T:= combinat:-cartprod([seq({-1, 1}, j = 1 .. n)]); b:= 0; while not T[finished] do    U := T[nextvalue]();    M := Matrix(n, shape = Circulant[U]);    d:= LinearAlgebra:-Determinant(M):    if d > b then b := d; end if; end do; return b; end proc: PROG (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 */ CROSSREFS Cf. A003433, A086432 (same for circulant (0,1) matrices), A215724 (same for (1,-1)-Toeplitz matrices). Cf. A215897 ( =a(n)/2^(n-1) ). Sequence in context: A131126 A159964 A058922 * A034918 A119003 A220329 Adjacent sequences:  A215720 A215721 A215722 * A215724 A215725 A215726 KEYWORD nonn,hard AUTHOR W. Edwin Clark, Aug 22 2012 EXTENSIONS a(16)-a(22) from Joerg Arndt, Aug 25 2012 a(23)-a(28) (as calculated by Warren Smith) from W. Edwin Clark, Sep 02 2012 STATUS approved

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Last modified May 24 18:12 EDT 2022. Contains 354043 sequences. (Running on oeis4.)