A003787 Order of universal Chevalley group A_n (3).

1, 24, 5616, 12130560, 237783237120, 42064805779476480, 67034222101339041669120, 961721214905722855895197286400, 124190524600592082795473760093457612800, 144339416867688029764487130056208182629053235200

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

• Geoffrey Critzer, Combinatorics of Vector Spaces over Finite Fields, Master's thesis, Emporia State University, 2018.
• Robert Steinberg, Lectures on Chevalley Groups, Dept. of Mathematics, Yale University, 1967, pp. 130-131.
• Index entries for sequences related to groups.

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