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%I #5 May 22 2013 20:33:26
%S 346,1389,6102,21182,141262,306574,607533,1969886,5266030,17975982,
%T 25750142,49814254,155091326,254757166,402919341,616863422,918109966,
%U 1109543806,2639036782,4871920766,6475547950,11018778302,14135789614,22598987966,42920581982
%N Number of conjugacy classes in simply connected twisted Chevalley group 2E6(q) as q runs through the prime powers.
%H Eric M. Schmidt, <a href="/A225934/b225934.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 + 11q^2 + 11q + 16 if q == (1 mod 6).
%F a(n) = q^6 + q^5 + 2q^4 + 18q^2 + 26q + 62 if q == (2 mod 6).
%F a(n) = q^6 + q^5 + 2q^4 + 11q^2 + 11q + 15 if q == (3 mod 6).
%F a(n) = q^6 + q^5 + 2q^4 + 10q^2 + 10q + 14 if q == (4 mod 6).
%F a(n) = q^6 + q^5 + 2q^4 + 19q^2 + 27q + 72 if q == (5 mod 6).
%o (Sage) def A225934(q) : return q^6 + q^5 + 2*q^4 + 4*q^3 + [11*q^2 + 11*q + 16, 18*q^2 + 26*q + 62, 11*q^2 + 11*q + 15, 10*q^2 + 10*q + 14, 19*q^2 + 27*q + 72][q%6-1]
%Y Cf. A188161, A224790, A225928 - A225938.
%K nonn
%O 1,1
%A _Eric M. Schmidt_, May 21 2013
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