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A374278 a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.

%I A374278 #12 Jul 07 2024 05:48:21
%S A374278 1,1,2,18,389,14284,798322,62490160,6519511313,873036867840,
%T A374278 145856387327074
%N A374278 a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
%H A374278 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%e A374278 a(5) = 14284:
%e A374278   [1, 4, 3, 2, 1]
%e A374278   [4, 1, 4, 3, 2]
%e A374278   [3, 4, 1, 4, 3]
%e A374278   [2, 3, 4, 1, 4]
%e A374278   [1, 2, 3, 4, 1]
%t A374278 a[0]=1; a[n_]:=Max[Table[Permanent[ToeplitzMatrix[Join[{1}, Part[Permutations[Range[n - 1]], i]]]], {i, (n-1)!}]]; Array[a, 11, 0]
%Y A374278 Cf. A351020, A374139, A374140 (minimal).
%Y A374278 Cf. A374239, A374240, A374241, A374242.
%K A374278 nonn,hard,more
%O A374278 0,3
%A A374278 _Stefano Spezia_, Jul 02 2024