A374070 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.

1, 0, 16, 192, 7056, 296928, 17353552, 1288517448, 123247560033, 14559205069230, 2068503986414344, 350413573991639400, 70216794936245622096, 16348540980271313405736, 4358673413318637872138056, 1324443244518891911978887758, 453726273130387432163560157389, 173630294056619179637594095141048

Offset: 0

Author

Stefano Spezia, Jun 27 2024

Keywords

• nonn

Examples

			a(4) = 7056:
  [0, 4, 6, 8]
  [4, 0, 4, 6]
  [6, 4, 0, 4]
  [8, 6, 4, 0]
		

Crossrefs

Cf. A071081 (determinant).

Cf. A374067, A374068, A374069, A374071.

Programs

Mathematica

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]]

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

Python

from sympy import Matrix, composite
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