A071081 -id:A071081 - cp's OEIS frontend

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

Stefano Spezia, Jun 27 2024

nonn

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

Cf. A071081 (determinant).

Cf. A374067, A374068, A374069, A374071.

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]]

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

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

A071080 Determinant of the n X n matrix whose element (i,j) equals the |i-j|-th composite number, or 1 if i=j.

Original entry on oeis.org

1, -15, 125, -935, 6096, -38340, 240864, -1497584, 8611328, -49201152, 277473280, -1541996288, 7852493824, -39972516864, 195624648704, -789661486080, 3052709008384, -9659706075392, 30089357409792, -63825905935360, 63965499203712, -8296932715920, -1139418909751008

Offset: 1

Robert G. Wilson v, May 26 2002

sign

Robert Israel, Table of n, a(n) for n = 1..1000

Cf. A071078, A071079, A071081, A071082, A071083.

Cf. A374069 (permanent).

comps:= remove(isprime,[$4 .. 1000]):
f:= proc(n) local M;
  M:= Matrix(n,n,(i,j) -> `if`(i=j,1,comps[abs(i-j)]));
  LinearAlgebra:-Determinant(M)
end proc:
map(f, [$1..25]); # Robert Israel, Dec 03 2024

Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; f[n_] := Det[ Table[ If[i == j, 1, Composite[ Abs[i - j]]], {i, 1, n}, {j, 1, n}]]; Table[ f[n], {n, 1, 20}]

a(21)-a(23) from Stefano Spezia, Jun 27 2024

cp's OEIS Frontend

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.

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