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 1-7 of 7 results.

A358569 a(n) is the minimal permanent of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1).

Original entry on oeis.org

1, 0, 1, 16, 451, 17376, 1022546
Offset: 0

Views

Author

Stefano Spezia, Nov 22 2022

Keywords

Comments

Also minimal permanent of an n X n Hankel matrix using the integers 0 to 2*(n - 1). - Stefano Spezia, Dec 22 2023

Examples

			a(2) = 1:
    [1, 0;
     2, 1]
a(3) = 16:
    [0, 1, 3;
     2, 0, 1;
     4, 2, 0]
		

Crossrefs

Cf. A350937 (integers from 1 to 2*n - 1), A358567 (minimal determinant), A358568 (maximal determinant), A358570 (maximal).

Extensions

a(5)-a(6) from Lucas A. Brown, Dec 03 2022

A358567 a(n) is the minimal determinant of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1).

Original entry on oeis.org

1, 0, -2, -31, -1297, -39837, -2256911, -99518694
Offset: 0

Views

Author

Stefano Spezia, Nov 22 2022

Keywords

Examples

			a(2) = -2:
    [0, 1;
     2, 0]
a(3) = -31:
    [2, 3, 0;
     4, 2, 3;
     1, 4, 2]
		

Crossrefs

Cf. A350930 (integers from 1 to 2*n - 1), A358568 (maximal), A358569 (minimal permanent), A358570 (maximal permanent).

Extensions

a(5)-a(7) from Lucas A. Brown, Dec 03 2022

A358568 a(n) is the maximal determinant of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1).

Original entry on oeis.org

1, 0, 4, 74, 1781, 58180, 2579770, 152337045
Offset: 0

Views

Author

Stefano Spezia, Nov 22 2022

Keywords

Examples

			a(2) = 4:
    [2, 0;
     1, 2]
a(3) = 74:
    [4, 0, 2;
     3, 4, 0;
     1, 3, 4]
		

Crossrefs

Cf. A350931 (integers from 1 to 2*n - 1), A358567 (minimal), A358569 (minimal permanent), A358570 (maximal permanent).

Extensions

a(5)-a(7) from Lucas A. Brown, Dec 03 2022

A368353 a(n) is the minimal determinant of an n X n Hankel matrix using the integers 0 to 2*(n - 1).

Original entry on oeis.org

1, 0, -4, -74, -1297, -39837
Offset: 0

Views

Author

Stefano Spezia, Dec 22 2023

Keywords

Comments

a(6) <= -2579770.

Examples

			a(2) = -4:
  1, 2;
  2, 0.
a(3) = -74:
  1, 3, 4;
  3, 4, 0;
  4, 0, 2.
a(4) = -1297:
  3, 2, 6, 0;
  2, 6, 0, 1;
  6, 0, 1, 4;
  0, 1, 4, 5.
		

Crossrefs

Cf. A368354 (maximal), A368355 (maximal absolute value).
Cf. A358569 (minimal permanent), A358570 (maximal permanent).

A368354 a(n) is the maximal determinant of an n X n Hankel matrix using the integers 0 to 2*(n - 1).

Original entry on oeis.org

1, 0, 2, 31, 1781, 58180
Offset: 0

Views

Author

Stefano Spezia, Dec 22 2023

Keywords

Comments

a(6) >= 2189560.

Examples

			a(2) = 2:
  2, 0;
  0, 1.
a(3) = 31:
  1, 4, 2;
  4, 2, 3;
  2, 3, 0.
a(4) = 1781:
  1, 2, 5, 6;
  2, 5, 6, 0;
  5, 6, 0, 4;
  6, 0, 4, 3.
		

Crossrefs

Cf. A368353 (minimal), A368355 (maximal absolute value).
Cf. A358569 (minimal permanent), A358570 (maximal permanent).

A368355 a(n) is the maximal absolute value of the determinant of an n X n Hankel matrix using the integers 0 to 2*(n - 1).

Original entry on oeis.org

1, 0, 4, 74, 1781, 58180
Offset: 0

Views

Author

Stefano Spezia, Dec 22 2023

Keywords

Comments

a(6) >= 2579770.

Examples

			a(2) = 4:
  1, 2;
  2, 0.
a(3) = 74:
  1, 3, 4;
  3, 4, 0;
  4, 0, 2.
a(4) = 1781:
  1, 2, 5, 6;
  2, 5, 6, 0;
  5, 6, 0, 4;
  6, 0, 4, 3.
		

Crossrefs

Cf. A368353 (minimal signed), A368354 (maximal signed).
Cf. A358569 (minimal permanent), A358570 (maximal permanent).

Formula

a(n) = max(-A368353(n), A368354(n)).

A369945 a(n) is the number of distinct values of the permanent of an n X n Hankel matrix using the integers 0 to 2*(n - 1).

Original entry on oeis.org

1, 1, 3, 39, 1710, 128502, 13644965
Offset: 0

Views

Author

Stefano Spezia, Feb 06 2024

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_] := CountDistinct[Table[Permanent[HankelMatrix[Join[Drop[per = Part[Permutations[Range[0, 2 n - 2]], i], n],{Part[per, n]}], Join[{Part[per, n]}, Drop[per, - n]]]], {i, (2 n - 1) !}]]; Join[{1},Array[a, 5]]
  • PARI
    a(n) = my(v=[0..2*n-2], list=List()); forperm(v, p, listput(list, matpermanent(matrix(n, n, i, j, p[i+j-1])));); #Set(list); \\ Michel Marcus, Feb 08 2024
    
  • Python
    from itertools import permutations
    from sympy import Matrix
    def A369945(n): return len({Matrix([p[i:i+n] for i in range(n)]).per() for p in permutations(range((n<<1)-1))}) # Chai Wah Wu, Feb 12 2024

Extensions

a(6) from Michel Marcus, Feb 08 2024
Showing 1-7 of 7 results.