On Sat, Aug 18, 2012 at 12:43 PM, Warren Smith <warren.wds@gmail.com> wrote:
What is the maximum |determinant| of an NxN circulant matrix whose defining first row consists entirely of +1's and -1's? (Related question: each entry lies between -1 and +1 inclusive?)
By changing slightly my (brute force) Maple program for http://oeis.org/A144926 for your question I get the following: 1, 1, [-1] 2, 0, 3, 4, [-1, -1, 1] 4, 16, [-1, -1, -1, 1] 5, 48, [-1, -1, -1, -1, 1] 6, 128, [-1, -1, -1, -1, -1, 1] 7, 512, [-1, -1, -1, 1, -1, 1, 1] 8, 2304, [-1, -1, -1, -1, 1, -1, 1, 1] 9, 6912, [-1, -1, -1, -1, -1, 1, -1, 1, 1] 10, 22528, [-1, -1, -1, -1, -1, -1, 1, -1, 1, 1] 11, 273408, [-1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1] 12, 2097152, [-1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1] 13, 14929920, [-1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1] 14, 50331648, [-1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1] 15, 390905856, [-1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1] The sequence 1, 0, 4, 16, 48, 128, 512, 2304, 6912, 22528, 273408, 2097152, 14929920, 50331648, 390905856 is apparently not in the OEIS.