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 1-5 of 5 results.

A374241 a(n) is the maximal absolute value of the determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.

Original entry on oeis.org

1, 1, 0, 1, 40, 545, 13805, 526773, 18551951, 768561384, 31451535983, 1273675677456, 87868166035113, 7601760995500947, 664087819207293468
Offset: 0

Views

Author

Stefano Spezia, Jul 01 2024

Keywords

Examples

			a(5) = 545:
  [1, 1, 4, 2, 3]
  [1, 1, 1, 4, 2]
  [4, 1, 1, 1, 4]
  [2, 4, 1, 1, 1]
  [3, 2, 4, 1, 1]

Links

Crossrefs

Cf. A351609, A374139.
Cf. A374239 (minimal), A374240 (maximal), A374242 (minimal nonzero absolute value).

Programs

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

Formula

a(n) = max(abs(A374239(n)), A374240(n)).

Extensions

a(11)-a(14) from Lucas A. Brown, Oct 10 2024

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]

Links

Crossrefs

Cf. A085750, A351609.
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)).

A351147 a(n) is the minimal determinant of a symmetric n X n matrix using the integers 1 to n*(n+1)/2.

Original entry on oeis.org

1, -7, -152, -6276, -550010, -94974369
Offset: 1

Views

Author

Hugo Pfoertner at the suggestion of Markus Sigg, Feb 15 2022

Keywords

Examples

			a(2) = -7:
  [1, 3;
   3, 2]
.
a(3) = -152:
  [5, 4, 1;
   4, 2, 6;
   1, 6, 3]
.
a(4) = -6276:
  [9,  5,  2,  4;
   5,  6, 10,  1;
   2, 10,  3,  7;
   4,  1,  7,  8]
.
a(5) = -550010:
  [ 3, 14,  7, 13,  9;
   14,  8,  1, 12,  4;
    7,  1,  6, 10, 15;
   13, 12, 10,  2, 11;
    9,  4, 15, 11,  5]
.
a(6) = -94974369:
  [ 5, 14,  7, 11, 21, 17;
   14, 12, 19,  3, 16,  1;
    7, 19, 13, 18,  2,  6;
   11,  3, 18, 10,  4, 20;
   21, 16,  2,  4,  9, 15;
   17,  1,  6, 20, 15,  8]

Crossrefs

Cf. A000217, A085000, A351148, A351609.

A351148 a(n) is the maximal determinant of a symmetric n X n matrix using the integers 1 to n*(n+1)/2.

Original entry on oeis.org

1, 5, 112, 7113, 745285, 90536348
Offset: 1

Views

Author

Hugo Pfoertner at the suggestion of Markus Sigg, Feb 15 2022

Keywords

Examples

			a(2) = 5:
  [2, 1;
   1, 3]
.
a(3) = 112:
  [1, 5, 4;
   5, 3, 6;
   4, 6, 2]
.
a(4) = 7113:
  [ 3, 10,  4,  8;
   10,  5,  1,  6;
    4,  1,  7,  9;
    8,  6,  9,  2]
.
a(5) = 745285:
  [10, 12,  1,  4, 13;
   12,  6,  5, 15,  3;
    1,  5,  9, 11, 14;
    4, 15, 11,  7,  2;
   13,  3, 14,  2,  8]
.
a(6) = 90536348:
  [18,  1,  7, 14,  6, 15;
    1, 13,  5, 17,  8, 20;
    7,  5, 12,  2, 21, 16;
   14, 17,  2, 11, 19,  3;
    6,  8, 21, 19,  9,  4;
   15, 20, 16,  3,  4, 10]

Crossrefs

Cf. A000217, A085000, A351147, A351609.

A358779 a(n) is the maximal absolute value of the determinant of an n X n symmetric matrix using all the integers from 0 to n*(n + 1)/2 - 1.

Original entry on oeis.org

1, 0, 4, 110, 5911, 652189, 86577891
Offset: 0

Views

Author

Stefano Spezia, Dec 05 2022

Keywords

Crossrefs

Cf. A000217, A351153, A351609.
Cf. A358806 (minimal determinant), A358807 (maximal determinant), A358808 (minimal permanent), A358809 (maximal permanent).

Formula

a(n) = max(abs(A358806(n)), A358807(n)).
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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