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A374281
a(n) is the maximal absolute value of the determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
5
1, 0, 1, 8, 44, 946, 27495, 592100, 25369920, 1246207300, 55400732937
OFFSET
0,4
FORMULA
a(n) = max(abs(A374279(n)), A374280(n)).
EXAMPLE
a(5) = 946:
[0, 1, 4, 2, 3]
[1, 0, 1, 4, 2]
[4, 1, 0, 1, 4]
[2, 4, 1, 0, 1]
[3, 2, 4, 1, 0]
MATHEMATICA
a[0]=1; a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{0}, Part[Permutations[Range[n-1]], i]]]]], {i, (n-1)!}]]; Array[a, 11, 0]
CROSSREFS
Cf. A085807 (minimal permanent), A374279 (minimal), A374280 (maximal), A374282 (minimal nonzero absolute value), A374283 (maximal permanent).
Sequence in context: A129553 A174643 A181268 * A361490 A075863 A118838
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Jul 02 2024
STATUS
approved