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.

A369830 a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix using the integers 1 to n.

Original entry on oeis.org

1, 1, 2, 5, 22, 97, 613, 4749, 38493, 353684
Offset: 0

Views

Author

Stefano Spezia, Feb 03 2024

Keywords

Links

Crossrefs

Cf. A000142, A350953, A350954, A356865.
Cf. A369831, A369832, A369833, A369834, A369835.

Programs

  • Mathematica
    a[n_] := CountDistinct[Table[Det[ToeplitzMatrix[Part[Permutations[Range[n]], i]]], {i, n !}]]; Join[{1}, Array[a,9]]
  • Python
    from itertools import permutations
from sympy import Matrix
def A369830(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).det() for p in permutations(range(1,n+1))}) # Chai Wah Wu, Feb 12 2024

Formula

a(n) <= A000142(n).

A369833 a(n) is the number of distinct values of the permanent of an n X n symmetric Toeplitz matrix using the first n prime numbers.

Original entry on oeis.org

1, 1, 1, 6, 24, 120, 720, 5040, 40320, 362880
Offset: 0

Views

Author

Stefano Spezia, Feb 03 2024

Keywords

Links

Crossrefs

Cf. A000142, A351021, A351022.
Cf. A369830, A369831, A369832, A369834, A369835.

Programs

  • Mathematica
    a[n_] := CountDistinct[Table[Permanent[ToeplitzMatrix[Part[Permutations[Prime[Range[n]]], i]]], {i, n !}]]; Join[{1}, Array[a,9]]
  • Python
    from itertools import permutations
from sympy import primerange, prime, Matrix
def A369833(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).per() for p in permutations(primerange(prime(n)+1))}) if n else 1 # Chai Wah Wu, Feb 11 2024

Formula

a(n) <= A000142(n).
Conjectured e.g.f.: 1/(1 - x) - x^2/2.

A369834 a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix using the integers 0 to n-1.

Original entry on oeis.org

1, 1, 2, 5, 23, 94, 614, 4628, 38243, 351024
Offset: 0

Views

Author

Stefano Spezia, Feb 03 2024

Keywords

Links

Crossrefs

Cf. A000142, A358323, A358324, A358325.
Cf. A369830, A369831, A369832, A369833, A369835.

Programs

  • Mathematica
    a[n_] := CountDistinct[Table[Det[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n - 1]]], i]]], {i, n !}]]; Join[{1}, Array[a,9]]
  • Python
    from itertools import permutations
from sympy import Matrix
def A369834(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).det() for p in permutations(range(n))}) # Chai Wah Wu, Feb 11 2024

Formula

a(n) <= A000142(n).

A369831 a(n) is the number of distinct values of the permanent of an n X n symmetric Toeplitz matrix using the integers 1 to n.

Original entry on oeis.org

1, 1, 1, 6, 23, 120, 720, 5040, 40320, 362880
Offset: 0

Views

Author

Stefano Spezia, Feb 03 2024

Keywords

Links

Crossrefs

Cf. A000142, A351019, A351020.
Cf. A369830, A369832, A369833, A369834, A369835.

Programs

  • Mathematica
    a[n_] := CountDistinct[Table[Permanent[ToeplitzMatrix[Part[Permutations[Range[n]],i]]], {i, n!}]]; Join[{1}, Array[a,9]]
  • Python
    from itertools import permutations
from sympy import Matrix
def A369831(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).per() for p in permutations(range(1,n+1))}) # Chai Wah Wu, Feb 12 2024

Formula

a(n) <= A000142(n).
Conjectured e.g.f.: 1/(1 - x) - x^2/2 - x^4/24.

A369835 a(n) is the number of distinct values of the permanent of an n X n symmetric Toeplitz matrix using the integers 0 to n-1.

Original entry on oeis.org

1, 1, 1, 6, 23, 119, 718, 5038, 40320, 362879
Offset: 0

Views

Author

Stefano Spezia, Feb 03 2024

Keywords

Links

Crossrefs

Cf. A000142, A358326, A358327.
Cf. A369830, A369831, A369832, A369833, A369834.

Programs

  • Mathematica
    a[n_] := CountDistinct[Table[Permanent[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n - 1]]], i]]], {i, n !}]]; Join[{1}, Array[a,9]]
  • Python
    from itertools import permutations
from sympy import Matrix
def A369835(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).per() for p in permutations(range(n))}) # Chai Wah Wu, Feb 11 2024

Formula

a(n) <= A000142(n).

A374619 a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the first n-1 primes off-diagonal.

Original entry on oeis.org

1, 1, 1, 2, 6, 22, 120, 717, 5039, 40312, 362874
Offset: 0

Views

Author

Stefano Spezia, Jul 14 2024

Keywords

Links

Crossrefs

Cf. A000142, A369832.
Cf. A374340, A374341, A374342, A374343.
Cf. A374617, A374618, A374620, A374621.

Programs

  • Mathematica
    a[n_]:=CountDistinct[Table[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]], i]]]], {i, (n -1)!}]]; Join[{1}, Array[a, 10]]

Formula

a(n) <= (n-1)! for n > 0.

A374620 a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal.

Original entry on oeis.org

1, 1, 1, 2, 6, 24, 120, 717, 5040, 40314, 362874
Offset: 0

Views

Author

Stefano Spezia, Jul 14 2024

Keywords

Links

Crossrefs

Cf. A000142, A369832.
Cf. A374386, A374387, A374388, A374389.
Cf. A374617, A374618, A374619, A374621.

Programs

  • Mathematica
    a[n_]:=CountDistinct[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]], i]]]], {i, (n -1)!}]]; Join[{1}, Array[a, 10]]

Formula

a(n) <= (n-1)! for n > 0.
Showing 1-7 of 7 results.

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