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A374620
a(n) is the number of distinct values 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.
4
1, 1, 1, 2, 6, 24, 120, 717, 5040, 40314, 362874
OFFSET
0,4
FORMULA
a(n) <= (n-1)! for n > 0.
MATHEMATICA
a[n_]:=CountDistinct[Table[Det[ToeplitzMatrix[Join[{0}, Part[Permutations[Prime[Range[n-1]]], i]]]], {i, (n -1)!}]]; Join[{1}, Array[a, 10]]
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Jul 14 2024
STATUS
approved