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 1-10 of 12 results. Next

A003837 Order of (usually) simple Chevalley group D_n (3).

Original entry on oeis.org

1, 144, 6065280, 4952179814400, 1289512799941305139200, 6762844700608770238252960972800, 11470635634813395742481912276441576767488000, 393736985584514548835738283681336315795223487793070080000
Offset: 1

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. A003830, A003838, A003839, A003840.

Programs

  • Mathematica
    d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}] / GCD[4, q^n-1]; Table[d[3, n], {n, 1, 8}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = d(3,n) where d(q,n) = D(q,n) / gcd(4, q^n-1) and D(q,n) as defined in A003830. - Sean A. Irvine, Sep 17 2015

Extensions

Fixed offset, one more term, and formula from Sean A. Irvine, Sep 17 2015

A003835 Order of universal Chevalley group D_n (8).

Original entry on oeis.org

7, 254016, 34558531338240, 19031213036231093492121600, 42863636354909175368011800612065142374400, 395357821818670720302212111102866352228895870285434270515200
Offset: 1

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. A003830, A003831, A003832, A003834, A003836.

Programs

  • Mathematica
    d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}]; Table[d[8, n], {n, 1, 8}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = D(8,n) where D(q,n) is defined in A003830. - Sean A. Irvine, Sep 17 2015
a(n) ~ c * 8^(n*(2*n-1)), where c = Product_{k>=1} (1 - 1/8^(2*k)) = 0.984130860306... . - Amiram Eldar, Jul 08 2025

A003847 Order of universal Chevalley group D_8(q), q = prime power.

Original entry on oeis.org

911666827031785075278550369566720000, 1574947942338058195342953134725345263180893951172280320000, 1649493899207759406688161287839326786813727965837588934265143296000000000
Offset: 1

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

Programs

  • Mathematica
    f[m_, n_] := m^(n (n - 1)) (m^n - 1) Product[m^(2 k) - 1, {k, n - 1}]; f[#, 8] & /@ Select[Range[2, 4], PrimePowerQ] (* Michael De Vlieger, Sep 17 2015 *)

Formula

a(n) = D(A000961(n+1),8) where D(q,n) is defined in A003830. Sean A. Irvine, Sep 17 2015

Extensions

a(3) added by Sean A. Irvine, Sep 17 2015

A003831 Order of universal Chevalley group D_n (4).

Original entry on oeis.org

3, 3600, 987033600, 67010895544320000, 1154606796534757164318720000, 5081732431326820541485324550799360000000, 5722569627753465177061732369386833143098255605760000000, 1649493899207759406688161287839326786813727965837588934265143296000000000
Offset: 1

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. A003830, A003832, A003834, A003835, A003836.

Programs

  • Maple
    a:= n -> 4^(n*(n-1))*(4^n-1)*mul(4^(2*k)-1, k=1..n-1):
seq(a(n), n=1..8);  # Alois P. Heinz, Jun 24 2025
  • Mathematica
    d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}]; Table[d[4, n], {n, 1, 8}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = D(4,n) where D(q,n) is defined in A003830. - Sean A. Irvine, Sep 17 2015
a(n) ~ c * 4^(n*(2*n-1)), where c = Product_{k>=1} (1 - 1/4^(2*k)) = 0.933594707399... . - Amiram Eldar, Jul 08 2025

A003832 Order of universal Chevalley group D_n (5).

Original entry on oeis.org

4, 14400, 29016000000, 35646156000000000000, 27230655539587500000000000000000, 12987912192212013697265625000000000000000000000, 3870897639595436240585697704315185546875000000000000000000000000
Offset: 1

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. A003830, A003831, A003834, A003835, A003836.

Programs

  • Mathematica
    d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}]; Table[d[5, n], {n, 1, 8}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = D(5,n) where D(q,n) is defined in A003830. - Sean A. Irvine, Sep 17 2015
a(n) ~ c * 5^(n*(2*n-1)), where c = Product_{k>=1} (1 - 1/5^(2*k)) = 0.958400102563... . - Amiram Eldar, Jul 08 2025

Extensions

a(7) from Sean A. Irvine, Sep 17 2015

A003834 Order of universal Chevalley group D_n (7).

Original entry on oeis.org

6, 112896, 4635182361600, 450219964711195607040000, 104772288945650279285144527564308480000, 58523113108854003897259712887271278079596939632967680000
Offset: 1

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. A003830, A003831, A003832, A003835, A003836.

Programs

  • Mathematica
    d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}]; Table[d[7, n], {n, 1, 8}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = D(7,n) where D(q,n) is defined in A003830. - Sean A. Irvine, Sep 17 2015
a(n) ~ c * 7^(n*(2*n-1)), where c = Product_{k>=1} (1 - 1/7^(2*k)) = 0.979175347148... . - Amiram Eldar, Jul 08 2025

A003836 Order of universal Chevalley group D_n (9).

Original entry on oeis.org

8, 518400, 203039372390400, 516728027484579221176320000, 8618734695485494933763249322971006238720000, 943067434111013598831873524092098584047517678156686295040000000
Offset: 1

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. A003830, A003831, A003832, A003834, A003835.

Programs

  • Mathematica
    d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}]; Table[d[9, n], {n, 1, 8}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = D(9,n) where D(q,n) is defined in A003830. - Sean A. Irvine, Sep 17 2015
a(n) ~ c * 9^(n*(2*n-1)), where c = Product_{k>=1} (1 - 1/9^(2*k)) = 0.987501905484... . - Amiram Eldar, Jul 08 2025

Extensions

a(6) from Sean A. Irvine, Sep 17 2015

A003846 Order of universal Chevalley group D_7(q), q = prime power.

Original entry on oeis.org

1691555775522928280469504000, 22941271269626791484963824552883153534976000, 5722569627753465177061732369386833143098255605760000000, 3870897639595436240585697704315185546875000000000000000000000000
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.
  • 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.

Links

Crossrefs

Cf. A000961, A003801, A003830, A003841, A003843, A003844, A003845, A003847.

Programs

  • Mathematica
    d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}]; Table[d[q, 7], {q, Select[Range[12], PrimePowerQ]}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = D(A000961(n+1),7) where D(q,n) is defined in A003830. - Sean A. Irvine, Sep 17 2015

A003841 Order of universal Chevalley group D_2(q), q = prime power.

Original entry on oeis.org

36, 576, 3600, 14400, 112896, 254016, 518400, 1742400, 4769856, 16646400, 23970816, 46785600, 147476736, 243360000, 386358336, 593409600, 885657600, 1071645696, 2561979456, 4744454400, 6314527296
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Numbers given so far divided by 36 (except the first) are all members of A014796. - Ralf Stephan, Feb 07 2004
Is a(n) = A007531( A000961(n)+1 )^2? - Ralf Stephan, Feb 08 2004 [Answer: Yes. This is equivalent to the first formula below. - Amiram Eldar, Jun 24 2025]

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. A000961, A003801, A003830, A003843, A003844, A003845, A003846, A003847, A007531, A014796.

Programs

  • Mathematica
    d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}]; Table[d[q, 2], {q, Select[Range[50], PrimePowerQ]}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = D(A000961(n+1),2) where D(q,n) is defined in A003830. - Sean A. Irvine, Sep 17 2015

A003843 Order of universal Chevalley group D_4(q), q = prime power.

Original entry on oeis.org

174182400, 19808719257600, 67010895544320000, 35646156000000000000, 450219964711195607040000, 19031213036231093492121600, 516728027484579221176320000, 142998501741091915820267520000
Offset: 1

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. A000961, A003801, A003830, A003841, A003844, A003845, A003846, A003847.

Programs

  • Mathematica
    d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}]; Table[d[q, 4], {q, Select[Range[12], PrimePowerQ]}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = D(A000961(n+1),4) where D(q,n) is defined in A003830. - Sean A. Irvine, Sep 17 2015
Showing 1-10 of 12 results. Next

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

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