OFFSET
1,2
COMMENTS
a(n) >= a(m)*a(n-m) for any m < n.
a(n) <= A003433(n), a bound achieved if the orthogonality requirement is dropped.
If there exists an order n Hadamard matrix, then a(n) = A003433(n) = n^(n/2).
For n == 2 (mod 4), if there exists an order n conference matrix (cf. A000952), then a(n) = (n-1)^(n/2). In particular, a(18) = 118587876497.
LINKS
Arun et al., Reference request: maximal determinant of matrices with pairwise orthogonal rows and entries in {1, 0, -1}, MathOverflow, 2022.
Wikipedia, Conference matrix.
Wikipedia, Hadamard matrix.
CROSSREFS
KEYWORD
hard,more,nonn
AUTHOR
Max Alekseyev, Mar 12 2022
EXTENSIONS
a(11)-a(14) from Max Alekseyev, May 20 2023
STATUS
approved