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a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the first n-1 primes off-diagonal.
5

%I #9 Jul 08 2024 08:38:33

%S 1,1,5,59,2454,177998,36960008,7670953632,2822399976144,

%T 1061085324952592,598646324654443008

%N a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the first n-1 primes off-diagonal.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.

%e a(5) = 177998:

%e [1, 7, 5, 3, 2]

%e [7, 1, 7, 5, 3]

%e [5, 7, 1, 7, 5]

%e [3, 5, 7, 1, 7]

%e [2, 3, 5, 7, 1]

%t a[n_]:=Max[Table[Permanent[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]

%Y Cf. A374067, A374278.

%Y Cf. A374340, A374341, A374342, A374343, A374067 (minimal).

%K nonn,hard,more

%O 0,3

%A _Stefano Spezia_, Jul 05 2024