A088853 -id:A088853 - cp's OEIS frontend

A088671 Number of n X n matrices over GF(3) with characteristic polynomial x^(n-1) * (x-1).

1, 12, 1053, 787320, 5208653241, 308413053837252, 164053436379620039253, 784901799876425497055472240, 33790882475498615361517892887614321, 13091723638887447119952122094399781435115772, 45648533143796439623892471646730372987043769546194573

Offset: 1

Yuval Dekel (dekelyuval(AT)hotmail.com) and W. Edwin Clark, Nov 29 2003

nonn

Irving Reiner, On the number of matrices with given characteristic polynomial, Illinois Journal of Mathematics, Vol. 5, No. 2 (1961), pp. 324-329.

Cf. A088668, A088852, A088853.

a[n_] := (3/2)*(3^(n^2-n) - 3^(n^2-2*n)); Array[a, 10] (* Amiram Eldar, Jul 13 2025 *)

a(n) = (q/(q-1))*(q^(n^2-n)-q^(-2*n+n^2)) where q = 3.

More terms from Joerg Arndt, Oct 04 2013

A088668 Number of n X n matrices over GF(2) with characteristic polynomial x^(n-1) * (x-1).

Original entry on oeis.org

1, 6, 112, 7680, 2031616, 2113929216, 8727373545472, 143552238122434560, 9426286221665580875776, 2473462226931531291448836096, 2594880778667185584863751461404672, 10886377285478460999082179823696022077440, 182665403921164334152319068371262729095485587456

Offset: 1

Yuval Dekel (dekelyuval(AT)hotmail.com) and W. Edwin Clark, Nov 29 2003

Irving Reiner, On the number of matrices with given characteristic polynomial, Illinois Journal of Mathematics, Vol. 5, No. 2 (1961), pp. 324-329.

Cf. A088671, A088852, A088853.

a[n_] := 2*(2^(n^2-n) - 2^(n^2-2*n)); Array[a, 10] (* Amiram Eldar, Jul 13 2025 *)

a(n)=(2^n-1)<<(n^2-2*n+1) \\ Charles R Greathouse IV, Oct 04 2013

a(n) = (q/(q-1))*(q^(n^2-n)-q^(-2*n+n^2)) where q = 2.

More terms from Joerg Arndt, Oct 04 2013

A088852 Number of n X n matrices over GF(4) with characteristic polynomial x^(n-1) * (x-1).

Original entry on oeis.org

1, 20, 5376, 22282240, 1464583847936, 1536853372840181760, 25788843362951132511993856, 6922956840496417818923870380359680, 29734213503918523875893136571995338085236736, 2043325439152335369940571764620635289780959288334745600

Offset: 1

Yuval Dekel (dekelyuval(AT)hotmail.com) and W. Edwin Clark, Nov 29 2003

nonn

Irving Reiner, On the number of matrices with given characteristic polynomial, Illinois Journal of Mathematics, Vol. 5, No. 2 (1961), pp. 324-329.

Cf. A088668, A088671, A088853.

a[n_] := (4/3)*(4^(n^2-n) - 4^(n^2-2*n)); Array[a, 10] (* Amiram Eldar, Jul 13 2025 *)

a(n) = (q/(q-1))*(q^(n^2-n)-q^(-2*n+n^2)) where q = 4.

More terms from Joerg Arndt, Oct 04 2013

cp's OEIS Frontend

A088671 Number of n X n matrices over GF(3) with characteristic polynomial x^(n-1) * (x-1).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A088668 Number of n X n matrices over GF(2) with characteristic polynomial x^(n-1) * (x-1).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A088852 Number of n X n matrices over GF(4) with characteristic polynomial x^(n-1) * (x-1).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions