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A374388
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 first n-1 primes off-diagonal.
5
1, 0, 4, 36, 324, 15164, 2287607, 162104000, 37905894000, 4059346088384, 718058901423168, 221630954408019520
OFFSET
0,3
FORMULA
a(n) = max(abs(A374386(n)), A374387(n)).
EXAMPLE
a(5) = 15164:
[0, 2, 7, 3, 5]
[2, 0, 2, 7, 3]
[7, 2, 0, 2, 7]
[3, 7, 2, 0, 2]
[5, 3, 7, 2, 0]
MATHEMATICA
a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{0}, Part[Permutations[Prime[Range[n-1]]], i]]]]], {i, (n-1)!}]]; Join[{1}, Array[a, 10]]
CROSSREFS
Cf. A374386 (minimal), A374387 (maximal), A374389 (minimal nonzero absolute value).
Cf. A374068 (minimal permanent), A374390 (maximal permanent).
Sequence in context: A000765 A226283 A270473 * A288269 A189334 A026334
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Jul 07 2024
EXTENSIONS
a(11) from Giorgos Kalogeropoulos, Jul 12 2024
STATUS
approved