A225932 - OEIS

%I #6 May 22 2013 20:32:44

%S 180,1269,6116,20454,140886,304548,605685,1965462,5262486,17969012,

%T 25736406,49802214,155060070,254728710,402876885,616803846,918054582,

%U 1109465220,2638941366,4871761782,6475396806,11018543046,14135564454,22598655270,42920128086

%N Number of conjugacy classes in simply connected Chevalley group E_6(q) as q runs through the prime powers.

%H Eric M. Schmidt, <a href="/A225932/b225932.txt">Table of n, a(n) for n = 1..1000</a>

%H Frank Luebeck, <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/chev/nrclasses/nrclasses.html">Numbers of Conjugacy Classes in Finite Groups of Lie Type</a>.

%F Let q be the n-th prime power.

%F a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 15q^2 + 21q + 60 if q == 1 (mod 6).

%F a(n) = q^6 + q^5 + 2q^4 + 2q^3 +  6q^2 +  4q +  4 if q == 2 (mod 6).

%F a(n) = q^6 + q^5 + 2q^4 + 2q^3 +  7q^2 +  5q +  3 if q == 3 (mod 6).

%F a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 14q^2 + 20q + 52 if q == 4 (mod 6).

%F a(n) = q^6 + q^5 + 2q^4 + 2q^3 +  7q^2 +  5q +  4 if q == 5 (mod 6).

%o (Sage) def A225932(q) : return q^6 + q^5 + 2*q^4 + 2*q^3 + [15*q^2 + 21*q + 60, 6*q^2 + 4*q + 4, 7*q^2 + 5*q + 3, 14*q^2 + 20*q + 52, 7*q^2 + 5*q + 4][q%6-1]

%Y Cf. A188161, A224790, A225928 - A225938.

%K nonn

%O 1,1

%A _Eric M. Schmidt_, May 21 2013