A351609 - OEIS

%I #11 Feb 18 2022 08:06:47

%S 1,1,7,152,7113,745285,94974369

%N Maximal absolute value of the determinant of an n X n symmetric matrix using the integers 1 to n*(n + 1)/2.

%C Upper bounds for the next terms can be found by considering all possibilities of choosing matrix entries on the diagonal and applying Gasper's determinant theorem (see references in A085000): a(7) <= 22475584128, a(8) <= 6634478203404, a(9) <= 2647044512044258. - _Hugo Pfoertner_, Feb 18 2022

%F a(n) = max(abs(A351147(n)), A351148(n)). - _Hugo Pfoertner_, Feb 16 2022

%e a(3) = 152:

%e    2    4    6

%e    4    5    1

%e    6    1    3

%e a(4) = 7113:

%e    2    6    8    9

%e    6    5   10    1

%e    8   10    3    4

%e    9    1    4    7

%Y Cf. A000217, A351147, A351148, A351153.

%Y Cf. A085000, A180128, A350931, A350933, A350954, A350956.

%K nonn,hard,more

%O 0,3

%A _Stefano Spezia_, Feb 14 2022

%E a(5)-a(6) from _Hugo Pfoertner_, Feb 16 2022