A003787 Order of universal Chevalley group A_n (3).

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

Offset

0,2

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

Table of n, a(n) for n=0..9.

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, p. 130-131.

Index entries for sequences related to groups

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

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 *)

Prog

(Magma) [&*[(3^n - 3^k): k in [0..n-1]]/2: n in [1..10]]; // Vincenzo Librandi, Sep 19 2015

Crossrefs

Sequence in context: A106207 A100089 A151598 * A002555 A239898 A002198

Adjacent sequences: A003784 A003785 A003786 * A003788 A003789 A003790

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved