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A374387
a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal.
5
1, 0, -4, 36, 129, 3340, 2287607, 162104000, 16943055268, 4059346088384, 474967482901952, 221630954408019520
OFFSET
0,3
EXAMPLE
a(5) = 3340:
[0, 5, 7, 3, 2]
[5, 0, 5, 7, 3]
[7, 5, 0, 5, 7]
[3, 7, 5, 0, 5]
[2, 3, 7, 5, 0]
MATHEMATICA
a[n_]:=Max[Table[Det[ToeplitzMatrix[Join[{0}, Part[Permutations[Prime[Range[n-1]]], i]]]], {i, (n-1)!}]]; Join[{1}, Array[a, 10]]
CROSSREFS
Cf. A374386 (minimal), A374388 (maximal absolute value), A374389 (minimal nonzero absolute value).
Cf. A374068 (minimal permanent), A374390 (maximal permanent).
Sequence in context: A045490 A318150 A275133 * A060783 A296948 A125756
KEYWORD
sign,hard,more
AUTHOR
Stefano Spezia, Jul 07 2024
EXTENSIONS
a(11) from Giorgos Kalogeropoulos, Jul 10 2024
STATUS
approved