A225930 - OEIS

%I #19 Jan 16 2025 11:29:45

%S 35,126,345,786,2806,4685,7386,16110,30946,69909,88746,137566,292566,

%T 406906,551886,732546,954310,1082405,1926226,2896410,3500206,4985766,

%U 5884906,8042226,12326286,14076610,17043525,20456446,25774710,28792666,39449446,43584810,48037086

%N Number of conjugacy classes in twisted Chevalley group 3D4(q) as q runs through the prime powers.

%H Paolo Xausa, <a href="/A225930/b225930.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Eric M. Schmidt)

%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. Then, a(n) = q^4 + q^3 + q^2 + q + c, where c = 5 if q is even and c = 6 if q is odd.

%t Map[(#^2 + 1)*(# + 1)*# + 5 + Mod[#, 2] &, Select[Range[100], PrimePowerQ]] (* _Paolo Xausa_, Jan 16 2025 *)

%o (PARI) apply(x->(x^4 + x^3 + x^2 + x + 5 + (x%2)), select(isprimepower, [1..100])) \\ _Michel Marcus_, Jan 16 2025

%Y Cf. A000961 (without 1), A188161, A224790, A225928-A225938.

%K nonn

%O 1,1

%A _Eric M. Schmidt_, May 21 2013