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 1-3 of 3 results.

A178795 Expansion of the polynomial (x^15-1)*(x^12-1)*(x^10-1)*(x^9-1)*(x^7-1)*(x^6-1)*(x^4-1)*(x-1) in increasing powers of x.

Original entry on oeis.org

1, -1, 0, 0, -1, 1, -1, 0, 1, -1, 1, 1, -2, 3, -1, -1, 3, -3, 1, 1, -4, 3, -1, -3, 4, -4, 1, 3, -5, 4, 0, -3, 6, -3, 0, 4, -5, 3, 1, -4, 4, -3, -1, 3, -4, 1, 1, -3, 3, -1, -1, 3, -2, 1, 1, -1, 1, 0, -1, 1, -1, 0, 0, -1, 1
Offset: 0

Views

Author

N. J. A. Sloane, Dec 26 2010

Keywords

Comments

q^120*(q^30-1)*(q^24-1)*(q^20-1)*(q^18-1)*(q^14-1)*(q^12-1)*(q^8-1)*(q^2-1) is the order of the simple group E_8(q), if q is a prime power.
If f(x) is the x-polynomial and g(q) the q-polynomial, then g(q) = q^120*f(q^2). - Jean-François Alcover, Aug 25 2022

Examples

			With p=2 one gets the order of E_8(2): 337804753143634806261388190614085595079991692242467651576160959909068800000. - _Jean-François Alcover_, Aug 25 2022

References

  • R. L. Griess, Jr., Twelve Sporadic Groups, Springer, 1998; see p. 169.

Links

Crossrefs

Cf. A009968, A178779, A178780, A178781.

Programs

  • PARI
    Vec((x^15-1)*(x^12-1)*(x^10-1)*(x^9-1)*(x^7-1)*(x^6-1)*(x^4-1)*(x-1)) \\ Michel Marcus, Aug 25 2022

A178780 Expansion of the polynomial x^36*(x^12-1)*(x^9-1)*(x^8-1)*(x^6-1)*(x^5-1)*(x^2-1) in increasing powers of x.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1, -1, 1, 0, -1, 1, 2, -1, 0, 3, 0, -2, 1, 1, -3, -1, 2, -1, -3, 1, 1, -2, 0, 3, 0, -1, 2, 1, -1, 0, 1, -1, -1, 0, 0, -1, 0, 1
Offset: 0

Views

Author

N. J. A. Sloane, Dec 26 2010

Keywords

Comments

q^36*(q^12-1)*(q^9-1)*(q^8-1)*(q^6-1)*(q^5-1)*(q^2-1) is the order of the simple group E_6(q), if q is a prime power.

References

  • R. L. Griess, Jr., Twelve Sporadic Groups, Springer, 1998; see p. 169.

Crossrefs

Cf. A008871, A178779, A178781, A178795.

A008869 Order of universal Chevalley group E_7 (q), q = prime power.

Original entry on oeis.org

7997476042075799759100487262680802918400, 2542750473636273484480959502278043289108758407541532509234790400
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.

Crossrefs

Cf. A178781.

Programs

  • Maple
    q^63*(q^2-1)*(q^6-1)*(q^8-1)*(q^10-1)*(q^12-1)*(q^14-1)*(q^18-1);
Showing 1-3 of 3 results.

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

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