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.

User: Steven E. Thornton

Steven E. Thornton's wiki page.

Steven E. Thornton has authored 24 sequences. Here are the ten most recent ones:

A306928 Number of different values taken by the determinant of a real (0,1,2) matrix of order n.

Original entry on oeis.org

1, 3, 9, 25, 67, 233, 893
Offset: 0

Author

Steven E. Thornton, Mar 16 2019

Keywords

Extensions

a(6) from Minfeng Wang, May 29 2024

A306818 Number of non-derogatory n X n matrices with elements {0, 1, 2}.

Original entry on oeis.org

3, 78, 19068, 42300060
Offset: 1

Author

Steven E. Thornton, Mar 11 2019

Keywords

Crossrefs

Number of characteristic polynomials is in A272659.
Number of minimal polynomials is in A306783.

A306816 Number of non-derogatory n X n matrices with elements {-1, 1}.

Original entry on oeis.org

2, 16, 472, 57456, 29025984
Offset: 1

Author

Steven E. Thornton, Mar 11 2019

Keywords

Crossrefs

Number of characteristic polynomials is in A272662.
Number of minimal polynomials is in A306782.

A306840 Number of singular n X n matrices with elements {0, 1, 2}.

Original entry on oeis.org

1, 31, 6891, 12202161, 175419087483, 20540753180392401
Offset: 1

Author

Steven E. Thornton, Mar 12 2019

Keywords

Crossrefs

Number of non-singular matrices is in A197487.

Extensions

a(6) from Minfeng Wang, May 29 2024

A306839 Number of unimodular n X n matrices with elements {-1, 0, 1}.

Original entry on oeis.org

2, 40, 6960, 10340736, 129599358720, 13527918439695360
Offset: 1

Author

Steven E. Thornton, Mar 12 2019

Keywords

Extensions

a(1)-a(5) confirmed and a(6) added by Minfeng Wang, May 01 2024

A306838 Number of different values taken by the determinant of a real (-1,0,1) matrix of order n.

Original entry on oeis.org

1, 3, 5, 9, 25, 67, 233
Offset: 0

Author

Steven E. Thornton, Mar 12 2019

Keywords

Comments

Every term in this sequence is odd, since 0 is a possible determinant, and if d is a possible determinant then so is -d.
a(n) >= 1 + 2^n, since every integer determinant between -2^(n-1) and 2^(n-1) is possible (see MathOverflow link).

Examples

			For n = 2, the possible determinants of a 2x2 matrix with entries from {-1,0,1} are -2, -1, 0, 1, and 2. Since there are 5 numbers in this list, a(2) = 5.
The possible nonnegative determinants for small values of n are as follows (all the negatives of these numbers are also possible determinants):
n = 1: 0, 1
n = 2: 0, 1, 2
n = 3: 0, 1, 2, 3, 4
n = 4: 0 through 10, 12, 16
n = 5: 0 through 28, 30, 32, 36, 40, 48
n = 6: 0 through 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 112, 114, 116, 120, 125, 128, 130, 132, 136, 144, 160
		

Crossrefs

Number of matrices having maximum determinant is in A051753.

Extensions

Edited and expanded by Nathaniel Johnston, Apr 19 2022
a(6) from Minfeng Wang, May 31 2024

A306837 Number of unimodular n X n matrices with elements {0, 1}.

Original entry on oeis.org

1, 6, 168, 20040, 9702720, 18480102480, 135491563468800, 3766962568171582080
Offset: 1

Author

Steven E. Thornton, Mar 12 2019

Keywords

Comments

An integer matrix is unimodular if its determinant is -1 or +1.

Crossrefs

Number of different values taken by the determinant is in A089472.
Maximum determinant is in A003432.
A363862 gives equivalence classes up to row and column permutation.

Extensions

a(7) and a(8) from Brendan McKay, Jun 25 2023

A306817 Number of non-derogatory n X n matrices with elements {-1, 0, 1}.

Original entry on oeis.org

3, 78, 18942, 41840168
Offset: 1

Author

Steven E. Thornton, Mar 11 2019

Keywords

Crossrefs

Number of characteristic polynomials is in A272658.
Number of minimal polynomials is in A271587.

A306815 Number of non-derogatory n X n matrices with elements {0, 1}.

Original entry on oeis.org

2, 14, 424, 54966, 28957764
Offset: 1

Author

Steven E. Thornton, Mar 11 2019

Keywords

Crossrefs

Number of characteristic polynomials is in A272661.
Number of minimal polynomials is in A306781.

A306820 Number of nilpotent n X n matrices with elements {-1, 0, 1}.

Original entry on oeis.org

1, 9, 481, 148817, 243782721
Offset: 1

Author

Steven E. Thornton, Mar 11 2019

Keywords

Crossrefs

Number of characteristic polynomials is in A272658.
Number of distinct eigenvalues is in A271570.