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a(n) is the permanent of the symmetric Toeplitz matrix of order n whose element (i,j) equals the |i-j|-th composite or 0 if i = j.
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%I #14 Jul 14 2024 15:15:19

%S 1,0,16,192,7056,296928,17353552,1288517448,123247560033,

%T 14559205069230,2068503986414344,350413573991639400,

%U 70216794936245622096,16348540980271313405736,4358673413318637872138056,1324443244518891911978887758,453726273130387432163560157389,173630294056619179637594095141048

%N a(n) is the permanent of the symmetric Toeplitz matrix of order n whose element (i,j) equals the |i-j|-th composite or 0 if i = j.

%e a(4) = 7056:

%e [0, 4, 6, 8]

%e [4, 0, 4, 6]

%e [6, 4, 0, 4]

%e [8, 6, 4, 0]

%t Composite[n_Integer]:=FixedPoint[n + PrimePi[#] + 1 &, n + PrimePi[n] + 1]; a[n_]:=Permanent[Table[If[i == j, 0, Composite[Abs[i - j]]], {i, 1, n}, {j, 1, n}]]; Join[{1},Array[a,17]]

%o (Python)

%o from sympy import Matrix, composite

%o def A374070(n): return Matrix(n,n,[composite(abs(j-k)) if j!=k else 0 for j in range(n) for k in range(n)]).per() if n else 1 # _Chai Wah Wu_, Jul 01 2024

%o (PARI) a(n) = my(composite(n)=my(k=-1); while(-n+n+=-k+k=primepi(n), ); n); matpermanent(matrix(n, n, i, j, if(i==j, 0, composite(abs(i-j))))); \\ _Ruud H.G. van Tol_, Jul 14 2024

%Y Cf. A071081 (determinant).

%Y Cf. A374067, A374068, A374069, A374071.

%K nonn

%O 0,3

%A _Stefano Spezia_, Jun 27 2024