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A374140 a(n) is the permanent of the symmetric Toeplitz matrix of order n whose element (i,j) equals abs(i-j) or 1 if i = j.

%I A374140 #15 Jul 05 2024 17:24:43
%S A374140 1,1,2,11,117,2083,55482,2063149,102176977,6490667261,514651043730,
%T A374140 49787897503031,5771746960693493,789652404867861919,
%U A374140 125885777192807718730,23129357587464094132601,4851600400570400272371009,1152232847579194480216644249,307579355879152834353840187554
%N A374140 a(n) is the permanent of the symmetric Toeplitz matrix of order n whose element (i,j) equals abs(i-j) or 1 if i = j.
%C A374140 Conjecture: a(n) is the minimal 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. - _Stefano Spezia_, Jul 05 2024
%e A374140 a(4) = 117:
%e A374140   [1, 1, 2, 3]
%e A374140   [1, 1, 1, 2]
%e A374140   [2, 1, 1, 1]
%e A374140   [3, 2, 1, 1]
%t A374140 a[n_]:=Permanent[Table[If[i == j, 1, Abs[i - j]], {i, n}, {j, n}]]; Join[{1}, Array[a, 18]]
%o A374140 (PARI) a(n) = matpermanent(matrix(n, n, i, j, if (i==j, 1, abs(i-j)))); \\ _Michel Marcus_, Jun 29 2024
%o A374140 (Python)
%o A374140 from sympy import Matrix
%o A374140 def A374140(n): return Matrix(n,n,[abs(j-k) if j!=k else 1 for j in range(n) for k in range(n)]).per() if n else 1 # _Chai Wah Wu_, Jul 01 2024
%Y A374140 Cf. A085807, A374067, A374139 (determinant).
%K A374140 nonn
%O A374140 0,3
%A A374140 _Stefano Spezia_, Jun 28 2024