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a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal.
4

%I #5 Jul 07 2024 13:49:06

%S 1,0,4,36,1936,144260,31972988,6800311204,2560967581304,

%T 975834087080060,557171087172087364

%N a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix having 0 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) = 144260:

%e [0, 7, 5, 3, 2]

%e [7, 0, 7, 5, 3]

%e [5, 7, 0, 7, 5]

%e [3, 5, 7, 0, 7]

%e [2, 3, 5, 7, 0]

%t a[n_]:=Max[Table[Permanent[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]

%Y Cf. A374345.

%Y Cf. A374386, A374387, A374388, A374389.

%Y Cf. A374068 (minimal permanent).

%K nonn,hard,more

%O 0,3

%A _Stefano Spezia_, Jul 07 2024