cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A374279 a(n) is the minimal determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.

Original entry on oeis.org

1, 0, -1, 4, -44, -946, -8281, -592100, -25369920, -511563816, -55400732937
Offset: 0

Views

Author

Stefano Spezia, Jul 02 2024

Keywords

Examples

			a(5) = -946:
  [0, 1, 4, 2, 3]
  [1, 0, 1, 4, 2]
  [4, 1, 0, 1, 4]
  [2, 4, 1, 0, 1]
  [3, 2, 4, 1, 0]
		

Crossrefs

Cf. A085807 (minimal permanent), A374280 (maximal), A374281 (maximal absolute value), A374282 (minimal nonzero absolute value), A374283 (maximal permanent).

Programs

  • Mathematica
    a[0]=1; a[n_]:=Min[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]],i]]]],{i,(n-1)!}]]; Array[a,11,0]

A374280 a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.

Original entry on oeis.org

1, 0, -1, 8, 28, 282, 27495, 581268, 17344692, 1246207300, 33366771123
Offset: 0

Views

Author

Stefano Spezia, Jul 02 2024

Keywords

Examples

			a(5) = 282:
  [0, 3, 4, 2, 1]
  [3, 0, 3, 4, 2]
  [4, 3, 0, 3, 4]
  [2, 4, 3, 0, 3]
  [1, 2, 4, 3, 0]
		

Crossrefs

Cf. A085807 (minimal permanent), A374279 (minimal), A374281 (maximal absolute value), A374282 (minimal nonzero absolute value), A374283 (maximal permanent).

Programs

  • Mathematica
    a[0]=1; a[n_]:=Max[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]],i]]]],{i,(n-1)!}]]; Array[a,11,0]

A374281 a(n) is the maximal absolute value of the determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.

Original entry on oeis.org

1, 0, 1, 8, 44, 946, 27495, 592100, 25369920, 1246207300, 55400732937
Offset: 0

Views

Author

Stefano Spezia, Jul 02 2024

Keywords

Examples

			a(5) = 946:
  [0, 1, 4, 2, 3]
  [1, 0, 1, 4, 2]
  [4, 1, 0, 1, 4]
  [2, 4, 1, 0, 1]
  [3, 2, 4, 1, 0]
		

Crossrefs

Cf. A085807 (minimal permanent), A374279 (minimal), A374280 (maximal), A374282 (minimal nonzero absolute value), A374283 (maximal permanent).

Programs

  • Mathematica
    a[0]=1; a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]],i]]]]],{i,(n-1)!}]]; Array[a,11,0]

Formula

a(n) = max(abs(A374279(n)), A374280(n)).

A374282 a(n) is the minimal absolute value of the determinant of a nonsingular n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.

Original entry on oeis.org

1, 4, 12, 2, 13, 16, 21, 4, 1
Offset: 2

Views

Author

Stefano Spezia, Jul 02 2024

Keywords

Comments

The offset is 2 because for n = 1 the matrix is null, and hence, singular.

Examples

			a(5) = 2:
  [0, 4, 1, 2, 3]
  [4, 0, 4, 1, 2]
  [1, 4, 0, 4, 1]
  [2, 1, 4, 0, 4]
  [3, 2, 1, 4, 0]
		

Crossrefs

Cf. A085807 (minimal permanent), A374279 (minimal signed), A374280 (maximal signed), A374281 (maximal absolute value), A374283 (maximal permanent).

Programs

  • Mathematica
    a[n_]:=Min[Select[Table[Abs[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]],i]]]]],{i,(n-1)!}],Positive]]; Array[a,9,2]
Showing 1-4 of 4 results.