cp's OEIS Frontend

A358324 a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1.

%I A358324 #11 Nov 19 2022 21:07:23
%S A358324 1,0,1,8,63,2090,36875,1123653,34292912,1246207300,53002204560,
%T A358324 2418538080316,215120941720912
%N A358324 a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1.
%H A358324 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A358323%2B4%2B5.py">Python program</a>.
%H A358324 Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%e A358324 a(3) = 8:
%e A358324     [0, 2, 1;
%e A358324      2, 0, 2;
%e A358324      1, 2, 0]
%e A358324 a(4) = 63:
%e A358324     [1, 3, 2, 0;
%e A358324      3, 1, 3, 2;
%e A358324      2, 3, 1, 3;
%e A358324      0, 2, 3, 1]
%e A358324 a(5) = 2090:
%e A358324     [2, 4, 0, 1, 3;
%e A358324      4, 2, 4, 0, 1;
%e A358324      0, 4, 2, 4, 0;
%e A358324      1, 0, 4, 2, 4;
%e A358324      3, 1, 0, 4, 2]
%t A358324 Join[{1}, Table[Max[Table[Det[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n-1]]], i]]],{i,n!}]],{n,9}]]
%Y A358324 Cf. A350954.
%Y A358324 Cf. A358323 (minimal), A358325 (minimal nonzero absolute value), A358326 (minimal permanent), A358327 (maximal permanent).
%K A358324 nonn,hard,more
%O A358324 0,4
%A A358324 _Stefano Spezia_, Nov 09 2022
%E A358324 a(10)-a(12) from _Lucas A. Brown_, Nov 16 2022