A002884 -id:A002884 - cp's OEIS frontend

A028365 Order of general affine group over GF(2), AGL(n,2).

1, 2, 24, 1344, 322560, 319979520, 1290157424640, 20972799094947840, 1369104324918194995200, 358201502736997192984166400, 375234700595146883504949480652800, 1573079924978208093254925489963584716800

Offset: 0

N. J. A. Sloane

For n > 0, a(n) = v(n+1)/v(n), where v = A203305 is the Vandermonde determinant of the first n of the numbers -2^j - 1; see the Mathematica section. - Clark Kimberling, Jan 01 2012

J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See p. 54 (1.64).

Seiichi Manyama, Table of n, a(n) for n = 0..57
Abdalla G. M. Ahmed, Matt Pharr, Victor Ostromoukhov, and Hui Huang, SZ Sequences: Binary-Based (0, 2^q)-Sequences, arXiv:2505.20434 [cs.GR], 2025. See p. 7.
Marcus Brinkmann, Extended Affine and CCZ Equivalence up to Dimension 4, Ruhr University Bochum (2019).
Putnam Competition 1999, Question A6, Amer. Math. Monthly 107 (Oct 2000), 721-732; see p. 725.
I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.

Cf. A000217, A002884, A005329, A020522, A048651, A053601, A203305.

[1] cat [(&*[2^(n+1) - 2^(j+1): j in [0..n-1]]): n in [1..20]]; // G. C. Greubel, Aug 31 2023

A028365 := n->2^n*product(2^n-2^'i','i'=0..n-1); # version 1
A028365 := n->product(2^'j'-1,'j'=1..n)*2^binomial(n+1,2); # version 2

RecurrenceTable[{a[1]==1, a[2]==2, a[3]==24, a[n]==(6a[n-1]^2 a[n-3] - 8a[n-1] a[n-2]^2)/(a[n-2] a[n-3])}, a[n], {n,20}] (* Harvey P. Dale, Aug 03 2011 *)
(* Next, the connection with Vandermonde determinants *)
f[j_]:= 2^j - 1; z = 15;
v[n_]:= Product[Product[f[k] - f[j], {j,k-1}], {k,2,n}]
Table[v[n], {n,z}]   (* A203303 *)
Table[v[n+1]/v[n], {n,z}]  (* A028365 *)
Table[v[n]*v[n+2]/(2*v[n+1])^2, {n,z}]  (* A171499 *) (* Clark Kimberling, Jan 01 2011 *)
Table[(-1)^n*2^Binomial[n+1,2]*QPochhammer[2,2,n], {n,0,20}] (* G. C. Greubel, Aug 31 2023 *)

a(n)=if(n<0,0,prod(k=1,n,2^k-1)*2^((n^2+n)/2)) /* Michael Somos, May 09 2005 */

[product(2^(n+1) - 2^(k+1) for k in range(n)) for n in range(21)] # G. C. Greubel, Aug 31 2023

a(n) is asymptotic to C*2^(n*(n+1)) where C = 0.288788095086602421278899721... = prod(k>=1, 1-1/2^k) (cf. A048651). - Benoit Cloitre, Apr 11 2003
a(n) = (6*a(n-1)^2*a(n-3) - 8*a(n-1)*a(n-2)^2) / (a(n-2)*a(n-3)). [From Putman Exam]. - Max Alekseyev, May 18 2007
a(n) = 2*A203305(n), n > 0. - Clark Kimberling, Jan 01 2012
From Max Alekseyev, Jun 09 2015: (Start)
a(n) = 2^A000217(n) * A005329(n).
a(n) = 2^n * A002884(n).
a(n) = 2^n * n! * A053601(n). (End)
From G. C. Greubel, Aug 31 2023: (Start)
a(n) = Product_{j=0..n-1} (2^(n+1) - 2^(j+1)).
a(n) = (-1)^n * 2^binomial(n+1,2) * QPochhammer(2,2,n). (End)

A046747 Number of n X n rational {0,1}-matrices of determinant 0.

Original entry on oeis.org

1, 10, 338, 42976, 21040112, 39882864736, 292604283435872, 8286284310367538176

Offset: 1

Günter M. Ziegler (ziegler(AT)math.tu-berlin.de)

			a(2)=10: the matrix of all 0's, 4 matrices with 2 zeros in the same row or column, 4 matrices with 3 zeros and the all-1 matrix.

J. Bourgain, V. Vu and P. M. Wood, On the Singularity Probability of Discrete Random Matrices, Journal of Functional Analysis, 258 (2010), 559-603.
R. P. Brent and J. H. Osborn, Bounds on minors of binary matrices, arXiv preprint arXiv:1208.3330 [math.CO], 2012.
J. Kahn, J. Komlos and E. Szemeredi, On the probability that a random ±1-matrix is singular, J. AMS 8 (1995), 223-240.
J. Komlos, On the determinant of (0,1)-matrices, Studia Math. Hungarica 2 (1967), 7-21.
N. Metropolis and P. R. Stein, On a class of (0,1) matrices with vanishing determinants, J. Combin. Theory, 3 (1967), 191-198.
Eric Weisstein's World of Mathematics, Singular Matrix.
Miodrag Zivkovic, Classification of small (0,1) matrices, arXiv:math/0511636 [math.CO], 2005.
Miodrag Zivkovic, Classification of small (0,1) matrices, Linear Algebra and its Applications, 414 (2006), 310-346.
Index entries for sequences related to binary matrices

Cf. A000409, A000410, A002416, A002884, A046747, A055165, A056989, A056990.

Sum[KroneckerDelta[Det[Array[Mod[Floor[k/(2^(n*(#1-1)+#2-1))],2]&,{n,n}]],0],{k,0,(2^(n^2))-1}] (* John M. Campbell, Jun 24 2011 *)
Count[Det /@ Tuples[{0, 1}, {n, n}], 0] (* David Trimas, Sep 23 2024 *)

A046747(n) = m=matrix(n,n); ct=0; for(x=0,2^(n*n)-1,a=binary(x+2^(n*n)); for(i=1,n, for(j=1,n,m[i,j]=a[n*i+j+1-n])); if(matdet(m)==0,ct=ct+1,); ); ct \\ Randall L Rathbun

a(n)=sum(i=0,2^n^2-1,matdet(matrix(n,n,x,y,(i>>(n*x+y-n-1))%2))==0) \\ Charles R Greathouse IV, Feb 21 2015

a(n) = 2^(n^2) - n! * binomial(2^n -1, n) + n! * A000410(n).
a(n) + A055165(n) = 2^(n^2) = total number of n X n (0, 1) matrices.
The probability that a random n X n {0,1}-matrix is singular is conjectured to be asymptotic to C(n+1, 2)*(1/2)^(n-1). [Corrected by N. J. A. Sloane, Jan 02 2007]

a(8) from Vladeta Jovovic, Mar 28 2006

A053291 Nonsingular n X n matrices over GF(4).

Original entry on oeis.org

1, 3, 180, 181440, 2961100800, 775476766310400, 3251791214634074112000, 218210695042457748180566016000, 234298374547168764346587444978647040000, 4025200069765920285793155323595159699896401920000, 1106437515026051855463365435310419366987397763763798016000000

Offset: 0

Stephen G Penrice, Mar 04 2000

Vincenzo Librandi, Table of n, a(n) for n = 0..40

Cf. A002884, A003788, A027637, A053763, A053290, A053292, A053293.

Cf. A100221, A115490.

[1] cat [&*[(4^n - 4^k): k in [0..n-1]]: n in [1..8]]; // Bruno Berselli, Jan 28 2013

Table[Product[4^n - 4^k, {k,0,n-1}], {n,0,10}] (* Geoffrey Critzer, Jan 26 2013 *)

for(n=0,10, print1(prod(k=0,n-1, 4^n - 4^k), ", ")) \\ G. C. Greubel, May 31 2018

a(n) = (4^n - 1)*(4^n - 4)*...*(4^n - 4^(n-1)).
a(n) = A053763(n)*A027637(n). - Bruno Berselli, Jan 30 2013
From Amiram Eldar, Jul 06 2025: (Start)
a(n) = Product_{k=1..n} A115490(k).
a(n) ~ c * 4^(n^2), where c = A100221. (End)

More terms from Vladeta Jovovic, Mar 16 2000

A053601 Number of bases of an n-dimensional vector space over GF(2).

Original entry on oeis.org

1, 1, 3, 28, 840, 83328, 27998208, 32509919232, 132640470466560, 1927943976061501440, 100981078400558897823744, 19242660536873338307044442112, 13448310596010038676027219703234560, 34707333779115158227208335860718444216320, 332718225878012276874300952228513073208156487680

Offset: 0

Fred Galvin (galvin(AT)math.ukans.edu), Jan 20 2000

			a(2)=3 because the 3 bases are {01,10}, {01,11}, {10,11}.

R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, Cambridge 1986

G. C. Greubel, Table of n, a(n) for n = 0..59
Claude Carlet, Philippe Gaborit, Jon-Lark Kim and Patrick Sole, A new class of codes for Boolean masking of cryptographic computations, arXiv:1110.1193 [cs.IT], 2011-2012.
David Ellerman, The number of direct-sum decompositions of a finite vector space, arXiv:1603.07619 [math.CO], 2016.
David Ellerman, The Quantum Logic of Direct-Sum Decompositions, arXiv:1604.01087 [quant-ph], 2016.

Cf. A002884.

[1] cat [(&*[2^n -2^k: k in [0..n-1]])/Factorial(n): n in [1..20]]; // G. C. Greubel, May 16 2019

Table[Product[2^n - 2^k, {k,0,n-1}]/n!, {n,0,20}] (* G. C. Greubel, May 16 2019 *)

a(n) = prod(k=0, n-1, 2^n - 2^k)/n!; \\ Michel Marcus, Mar 25 2016

[product(2^n -2^k for k in (0..n-1))/factorial(n) for n in (0..20)] # G. C. Greubel, May 16 2019

a(n) = (2^n-1)(2^n-2)...(2^n-2^(n-1))/n! = A002884(n)/n!.

More terms from Vladeta Jovovic, Apr 05 2000

A053292 Number of nonsingular n X n matrices over GF(5).

Original entry on oeis.org

1, 4, 480, 1488000, 116064000000, 226614960000000000, 11064475422000000000000000, 13506266841692625000000000000000000, 412177498341354683437500000000000000000000000

Offset: 0

Stephen G Penrice, Mar 04 2000

Vincenzo Librandi, Table of n, a(n) for n = 0..35
Jeffrey Overbey, William Traves, and Jerzy Wojdylo, On the Keyspace of the Hill Cipher, Cryptologia, Vol. 29, Iss. 1 (2005), pp. 59-72; author's copy.

Column k=5 of A316622.

Cf. A002884, A003789, A027872, A053290, A053291, A053293, A109345, A100222.

[1] cat [&*[(5^n - 5^k): k in [0..n-1]]: n in [1..8]]; // Bruno Berselli, Jan 28 2013

Table[Product[5^n - 5^k, {k,0,n-1}], {n,0,10}] (* Geoffrey Critzer, Jan 26 2013 *)

for(n=0,10, print1(prod(k=0,n-1, 5^n - 5^k), ", ")) \\ G. C. Greubel, May 31 2018

a(n) = (5^n - 1)*(5^n - 5)*...*(5^n - 5^(n-1)).
a(n) = A109345(n)*A027872(n). - Bruno Berselli, Jan 30 2013
a(n) ~ c * 5^(n^2), where c = A100222. - Amiram Eldar, Jul 06 2025

More terms from Vladeta Jovovic, Mar 16 2000

A053293 Number of nonsingular n X n matrices over GF(7).

Original entry on oeis.org

1, 6, 2016, 33784128, 27811094169600, 1122211189922928537600, 2218959336124989671614429593600, 214992513152176999576908105619651923148800, 1020690003311610463765638355505358381593396977336320000, 237443634207909205360438080389756681126654524500073656592021585920000

Offset: 0

Stephen G Penrice, Mar 04 2000

Vincenzo Librandi, Table of n, a(n) for n = 0..30
Jeffrey Overbey, William Traves, and Jerzy Wojdylo, On the Keyspace of the Hill Cipher, Cryptologia, Vol. 29, Iss. 1 (2005), pp. 59-72; author's copy.

Column k=7 of A316622.

Cf. A002884, A003790, A027875, A053290, A053291, A053292, A109493, A132035.

[1] cat [&*[(7^n - 7^k): k in [0..n-1]]: n in [1..7]]; // Bruno Berselli, Jan 28 2013

Table[Product[7^n - 7^k, {k, 0, n-1}], {n, 0, 10}] (* Vincenzo Librandi, Jan 28 2013 *)

for(n=0,10, print1(prod(k=0,n-1, 7^n - 7^k), ", ")) \\ G. C. Greubel, May 31 2018

a(n) = (7^n - 1)*(7^n - 7)*...*(7^n - 7^(n-1)).
a(n) = A109493(n)*A027875(n). - Bruno Berselli, Jan 30 2013
a(n) ~ c * 7^(n^2), where c = A132035. - Amiram Eldar, Jul 06 2025

More terms from Vladeta Jovovic, Mar 16 2000

A132186 Number of idempotent n X n matrices over GF(2); also number of diagonalizable n X n matrices over GF(2).

Original entry on oeis.org

1, 2, 8, 58, 802, 20834, 1051586, 102233986, 19614424834, 7355623374338, 5494866505497602, 8087844439442585602, 23834930674299549249538, 138978138716920276085366786, 1626809921636911219317749563394, 37757678575184051755732304668884994

Offset: 0

Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 19 2003 and Vladeta Jovovic, Nov 04 2007

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..81
Geoffrey Critzer, Combinatorics of Vector Spaces over Finite Fields, Master's thesis, Emporia State University, 2018.
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

Cf. A002884, A081080.

Row sums of A296548.

T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
      `if`(n=0, 1, T(n-1, k-1)+2^k*T(n-1, k)))
    end:
a:= n-> add(2^(k*(n-k))*T(n, k), k=0...n):
seq(a(n), n=0..20);  # Alois P. Heinz, Aug 06 2017

nn = 10; g[n_] := (q - 1)^n  q^Binomial[n, 2] FunctionExpand[
QFactorial[n, q]] /. q -> 2; G[z_] := Sum[z^k/g[k], {k, 0, nn}];Table[g[n], {n, 0, nn}] CoefficientList[Series[G[z]^2, {z, 0, nn}], z] (* Geoffrey Critzer, Aug 04 2017 *)
a[n_] := Block[{m}, Length@ Select[ Range[2^(n^2)], (m = Partition[ IntegerDigits[ #-1, 2, n^2], n]; Mod[m.m, 2] == m) &]]; a /@ Range[4] (* Giovanni Resta, Apr 09 2017 *)

a(n) = sum(k=0...n, 2^(k(n-k))*[n,k]2), where [n,k]_2 is the Gaussian binomial for q=2. - _Marc van Leeuwen, May 22 2013
a(n)/A002884(n) is the coefficient of x^n in (Sum_{n>=0} x^n/A002884(n))^2. - Geoffrey Critzer, Aug 04 2017
a(n) ~ c * 2^(n^2/2), where c = EllipticTheta(3, 0, 1/4) / QPochhammer(1/2) = 5.221199057419682876170323638731707664618893... if n is even and c = EllipticTheta(2, 0, 1/4) / QPochhammer(1/2) = 5.2043255482837364968664526298606149440286... if n is odd. - Vaclav Kotesovec, Jun 09 2025

This is the result of merging two independently submitted but identical sequences. Thanks to Geoffrey Critzer for suggesting this. - N. J. A. Sloane, Dec 26 2017

A002820 Number of n X n invertible binary matrices A such that A+I is invertible.

Original entry on oeis.org

1, 0, 2, 48, 5824, 2887680, 5821595648, 47317927329792, 1544457148312846336, 202039706313624586813440, 105823549214125066767168438272, 221819704567105547916502447159246848, 1860304261534304703934696550224148083769344, 62413833036707798343389591015829588620560344023040

Offset: 0

N. J. A. Sloane

Also number of linear orthomorphisms of GF(2)^n.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vincenzo Librandi, Table of n, a(n) for n = 0..55
Zong Duo Dai, Solomon W. Golomb, and Guang Gong, Generating all linear orthomorphisms without repetition, Discrete Math. 205 (1999), 47-55.
P. F. Duvall, Jr. and P. W. Harley, III, A note on counting matrices, SIAM J. Appl. Math., 20 (1971), 374-377.
Hsien-Kuei Hwang, Emma Yu Jin, and Michael J. Schlosser, Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow, arXiv:2012.13570 [math.CO], 2020.
Kent Morrison, Matrices over F_q with no eigenvalues of 0 or 1
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
Index entries for sequences related to binary matrices

Cf. A002884.

Column k=0 of A346201 and of A346381.

# (Maple program based on Dai et al. from N. J. A. Sloane, Aug 10 2011)
N:=proc(n,i) option remember; if i = 1 then 1 else (2^n-2^(i-1))*N(n,i-1); fi; end;
Oh:=proc(n) option remember; local r; global N;
if n=0 then RETURN(1) elif n=1 then RETURN(0) else
add( 2^(r-2)*N(n,r)*2^(r*(n-r))*Oh(n-r), r=2..n); fi; end;
[seq(Oh(n),n=0..15)];

ni[n_, i_] := ni[n, i] = If[i == 1, 1, (2^n - 2^(i-1))*ni[n, i-1]]; a[0] = 1; a[1] = 0; a[n_] := a[n] = Sum[ 2^(r-2)*ni[n, r]*2^(r*(n-r))*a[n-r], {r, 2, n}]; Table[a[n], {n, 1, 11}] (* Jean-François Alcover, Jan 19 2012, after Maple *)

Reference gives a recurrence.

a(n) = 2^(n(n-1)/2) * A005327(n+1).

More terms from Vladeta Jovovic, Mar 17 2000
Entry revised by N. J. A. Sloane, Aug 10 2011
a(0)=1 prepended by Alois P. Heinz, Jan 10 2025

A316622 Array read by antidiagonals: T(n,k) is the order of the group GL(n,Z_k).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 6, 1, 1, 2, 48, 168, 1, 1, 4, 96, 11232, 20160, 1, 1, 2, 480, 86016, 24261120, 9999360, 1, 1, 6, 288, 1488000, 1321205760, 475566474240, 20158709760, 1, 1, 4, 2016, 1886976, 116064000000, 335522845163520, 84129611558952960, 163849992929280, 1

Offset: 0

Andrew Howroyd, Jul 08 2018

All rows are multiplicative.
Equivalently, the number of invertible n X n matrices mod k.
Also, for k prime (but not higher prime powers) the number of nonsingular n X n matrices over GF(k).
For k >= 2, n! divides T(n,k) since the subgroup of GL(n,k) consisting of all permutation matrices is isomorphic to S_n (the n-th symmetric group). Note that a permutation matrix is an orthogonal matrix, hence having determinant +-1. - Jianing Song, Oct 29 2022

			Array begins:
=================================================================
n\k| 1       2         3          4             5           6
---+-------------------------------------------------------------
0  | 1       1         1          1            1            1 ...
1  | 1       1         2          2            4            2 ...
2  | 1       6        48         96          480          288 ...
3  | 1     168     11232      86016      1488000      1886976 ...
4  | 1   20160  24261120 1321205760 116064000000 489104179200 ...
5  | 1 9999360  ...
...

R. P. Brent and B. D. McKay, Determinants and ranks of random matrices over Zm, Discrete Mathematics 66 (1987) pp. 35-49.
J. M. Lockhart and W. P. Wardlaw, Determinants of Matrices over the Integers Modulo m, Mathematics Magazine, Vol. 80, No. 3 (Jun., 2007), pp. 207-214.
The Group Properties Wiki, Order formulas for linear groups

Rows n=2..4 are A000252, A064767, A305186.
Columns k=2..7 are A002884, A053290, A065128, A053292, A065498, A053293.
Cf. A053291 (GF(4)), A052496 (GF(8)), A052497 (GF(9)).
Cf. A316623.

T:=function(n,k) if k=1 or n=0 then return 1; else return Order(GL(n, Integers mod k)); fi; end;
for n in [0..5] do Print(List([1..6], k->T(n,k)), "\n"); od;

T[, 1] = T[0, ] = 1; T[n_, k_] := T[n, k] = Module[{f = FactorInteger[k], p, e}, If[Length[f] == 1, {p, e} = f[[1]]; (p^e)^(n^2)* Product[(1 - 1/p^j), {j, 1, n}], Times @@ (T[n, Power @@ #]& /@ f)]];
Table[T[n - k + 1, k], {n, 0, 8}, {k, n + 1, 1, -1}] // Flatten (* Jean-François Alcover, Jul 25 2019 *)

T(n,k)={my(f=factor(k)); k^(n^2) * prod(i=1, #f~, my(p=f[i,1]); prod(j=1, n, (1 - p^(-j))))}

T(n,p^e) = (p^e)^(n^2) * Product_{j=1..n} (1 - 1/p^j) for prime p.

A171499 a(n) = 6a(n-1) - 8a(n-2) for n > 1; a(0) = 3, a(1) = 14.

Original entry on oeis.org

3, 14, 60, 248, 1008, 4064, 16320, 65408, 261888, 1048064, 4193280, 16775168, 67104768, 268427264, 1073725440, 4294934528, 17179803648, 68719345664, 274877644800, 1099511103488, 4398045462528, 17592183947264, 70368739983360

Offset: 0

Klaus Brockhaus, Dec 10 2009

Binomial transform of A171498; second binomial transform of A171497; third binomial transform of A010703.
Related to sequences A001969 and A000069, sum of each group with exponent 1. - Eric Desbiaux, Jul 24 2013
a(n) in base 2 is n+2 1s followed by n 0s. - Hussam al-Homsi, Oct 12 2021

Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (6,-8).

Cf. A010703, A171472, A171473, A171476, A171497, A171498.

[4*4^n-2^n: n in [0..30]]; // Vincenzo Librandi, Jul 18 2011

(* This program shows how A171499 arises from the Vandermonde determinant of (1,2,4,...,2^(n-1)). *)
f[j_]:= 2^j - 1; z = 15;
v[n_]:= Product[Product[f[k] - f[j], {j,k-1}], {k,2,n}]
d[n_]:= Product[(i-1)!, {i,n}]
Table[v[n], {n,z}]                     (* A203303 *)
Table[v[n+1]/v[n], {n,z}]              (* A002884 *)
Table[v[n]*v[n+2]/(2*v[n+1])^2, {n,z}]  (* A171499 *)
(* Clark Kimberling, Jan 02 2011 *)
LinearRecurrence[{6,-8},{3,14},30] (* Harvey P. Dale, Sep 05 2021 *)

{m=23; v=concat([3, 14], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]); v}

[4^(n+1) -2^n for n in range(31)] # G. C. Greubel, Aug 31 2023

a(n) = 4*4^n - 2^n = 2^n * (2^(n+2) - 1).
G.f.: (3-4*x)/((1-2*x)*(1-4*x)).
a(n) = 4*a(n-1) + 2^n for n > 0. - Vincenzo Librandi, Jul 18 2011
a(n) = A171476(n+1)/2. - Hussam al-Homsi, Jun 06 2021
E.g.f.: 4*exp(4*x) - exp(2*x). - G. C. Greubel, Aug 31 2023

cp's OEIS Frontend

A028365 Order of general affine group over GF(2), AGL(n,2).

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A046747 Number of n X n rational {0,1}-matrices of determinant 0.

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A053291 Nonsingular n X n matrices over GF(4).

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A053601 Number of bases of an n-dimensional vector space over GF(2).

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Magma

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Sage

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A053292 Number of nonsingular n X n matrices over GF(5).

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Magma

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PARI

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A053293 Number of nonsingular n X n matrices over GF(7).

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Magma

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A171499 a(n) = 6a(n-1) - 8a(n-2) for n > 1; a(0) = 3, a(1) = 14.