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 1-6 of 6 results.

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

Views

Author

Stephen G Penrice, Mar 04 2000

Keywords

Links

Crossrefs

Cf. A002884, A003788, A027637, A053763, A053290, A053292, A053293.
Cf. A100221, A115490.

Programs

  • Magma
    [1] cat [&*[(4^n - 4^k): k in [0..n-1]]: n in [1..8]]; // Bruno Berselli, Jan 28 2013
  • Mathematica
    Table[Product[4^n - 4^k, {k,0,n-1}], {n,0,10}] (* Geoffrey Critzer, Jan 26 2013 *)
  • PARI
    for(n=0,10, print1(prod(k=0,n-1, 4^n - 4^k), ", ")) \\ G. C. Greubel, May 31 2018

Formula

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)

Extensions

More terms from Vladeta Jovovic, Mar 16 2000

A003787 Order of universal Chevalley group A_n (3).

Original entry on oeis.org

1, 24, 5616, 12130560, 237783237120, 42064805779476480, 67034222101339041669120, 961721214905722855895197286400, 124190524600592082795473760093457612800, 144339416867688029764487130056208182629053235200
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
  • H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

Links

Crossrefs

Cf. A003788, A003789, A003790, A003791, A003792, A053290, A100220.

Programs

  • Magma
    [&*[(3^n - 3^k): k in [0..n-1]]/2: n in [1..10]]; // Vincenzo Librandi, Sep 19 2015
  • Mathematica
    f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}];
f[3, #] & /@ Range[0, 9] (* Michael De Vlieger, Sep 18 2015 *)

Formula

Numbers so far appear to equal A053290(n)/2. - Ralf Stephan, Mar 30 2004
a(n) = A(3,n) where A(q,n) = q^(n*(n+1)/2) * Product_{k=2..n+1}(q^k-1). - Sean A. Irvine, Sep 18 2015
a(n) ~ c * 3^(n*(n+2)), where c = (3/2) * A100220 = 0.840189116891... . - Amiram Eldar, Jul 07 2025

Extensions

One more term from Sean A. Irvine, Sep 18 2015

A003789 Order of universal Chevalley group A_n (5).

Original entry on oeis.org

1, 120, 372000, 29016000000, 56653740000000000, 2766118855500000000000000, 3376566710423156250000000000000000, 103044374585338670859375000000000000000000000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
  • H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

Links

Crossrefs

Cf. A003787, A003788, A003790, A003791, A003792, A053292, A100222.

Programs

  • Magma
    [&*[(5^n-5^k): k in [0..n-1]]/4: n in [1..8]]; // Vincenzo Librandi, Sep 19 2015
  • Mathematica
    f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}]; f[5, #] & /@ Range[0, 7] (* Michael De Vlieger, Sep 18 2015 *)

Formula

Numbers so far appear to equal A053292(n)/4. - Ralf Stephan, Mar 30 2004
a(n) = A(5,n) where A(q,n) is defined in A003787. - Sean A. Irvine, Sep 18 2015
a(n) ~ c * 5^(n*(n+2)), where c = (5/4) * A100222 = 0.950415994839... . - Amiram Eldar, Jul 07 2025

A003790 Order of universal Chevalley group A_n (7).

Original entry on oeis.org

1, 336, 5630688, 4635182361600, 187035198320488089600, 369826556020831611935738265600, 35832085525362833262818017603275320524800, 170115000551935077294273059250893063598899496222720000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
  • H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

Links

Crossrefs

Cf. A003787, A003788, A003789, A003791, A003792,A053293, A100220.

Programs

  • Magma
    [&*[(7^n - 7^k): k in [0..n-1]]/6: n in [1..10]]; // Vincenzo Librandi, Sep 19 2015
  • Mathematica
    f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}]; f[7, #] & /@ Range[0, 7] (* Michael De Vlieger, Sep 18 2015 *)

Formula

Numbers so far appear to equal A053293(n)/6. - Ralf Stephan, Mar 30 2004
a(n) = A(7,n) where A(q,n) is defined in A003787. - Sean A. Irvine, Sep 18 2015
a(n) ~ c * 7^(n*(n+2)), where c = (7/6) * A100220 = 0.840189116891... . - Amiram Eldar, Jul 07 2025

Extensions

a(7) from Sean A. Irvine, Sep 18 2015

A003792 Order of universal Chevalley group A_n (9).

Original entry on oeis.org

1, 720, 42456960, 203039372390400, 78660280796419613491200, 2468438315722201136962330755072000, 6274437692242927471137606015213542491815936000, 1291851049702792234730057308758464452124128263449062932480000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
  • H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

Links

Crossrefs

Cf. A003787, A003788, A003789, A003790, A003791, A052497, A132037.

Programs

  • Magma
    [&*[(9^n - 9^k): k in [0..n-1]]/8: n in [1..10]]; // Vincenzo Librandi, Sep 19 2015
  • Mathematica
    f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}];
f[9, #] & /@ Range[0, 7] (* Michael De Vlieger, Sep 18 2015 *)

Formula

Numbers so far appear to equal A052497(n)/8. - Ralf Stephan, Mar 30 2004
a(n) = A(9,n) where A(q,n) is defined in A003787. - Sean A. Irvine, Sep 18 2015
a(n) ~ c * 9^(n*(n+2)), where c = (9/8) * A132037 = 0.9861303982904... . - Amiram Eldar, Jul 07 2025

Extensions

a(7) from Sean A. Irvine, Sep 18 2015

A003791 Order of universal Chevalley group A_n (8).

Original entry on oeis.org

1, 504, 16482816, 34558531338240, 4638226007491010887680, 39841906041871272087686291128320, 21903309038581548352789123727634573903790080
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
  • H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

Links

Crossrefs

Cf. A003787, A003788, A003789, A003790, A003792, A052496, A132036.

Programs

  • Magma
    [&*[(8^n - 8^k): k in [0..n-1]]/7: n in [1..8]]; // Vincenzo Librandi, Sep 19 2015
  • Mathematica
    f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}]; f[8, #] & /@ Range[0, 6] (* Michael De Vlieger, Sep 18 2015 *)

Formula

Numbers so far appear to equal A052496(n)/7. - Ralf Stephan, Mar 30 2004
a(n) = A(8,n) where A(q,n) is defined in A003787. - Sean A. Irvine, Sep 18 2015
a(n) ~ c * 8^(n*(n+2)), where c = (8/7) * A132036 = 0.982178279315... . - Amiram Eldar, Jul 07 2025
Showing 1-6 of 6 results.

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

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