cp's OEIS Frontend

A225936 Number of conjugacy classes in simply connected Chevalley group E_7(q) as q runs through the prime powers.

%I A225936 #7 May 22 2013 20:34:06
%S A225936 531,5052,24553,107833,999759,2447517,5494392,21711067,68562129,
%T A225936 287617189,437995549,946912755,3567919999,6370211253,10880553708,
%U A225936 17891119105,28464383127,35505127221,97650322329,199757104357,278459342139,517897029319,692671751805
%N A225936 Number of conjugacy classes in simply connected Chevalley group E_7(q) as q runs through the prime powers.
%H A225936 Eric M. Schmidt, <a href="/A225936/b225936.txt">Table of n, a(n) for n = 1..1000</a>
%H A225936 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 A225936 Let q be the n-th prime power. Then, a(n) is
%F A225936 q^7 + q^6 + 2q^5 + 4q^4 + 10q^3 + 15q^2 + 25q + 21 if q == 0 (mod 2);
%F A225936 q^7 + q^6 + 2q^5 + 7q^4 + 17q^3 + 35q^2 + 70q + 99 if q == 0 (mod 3);
%F A225936 q^7 + q^6 + 2q^5 + 7q^4 + 17q^3 + 35q^2 + 71q + 103 otherwise.
%o A225936 (Sage) def A225936(q) : return q^7 + q^6 + 2*q^5 + (4*q^4 + 10*q^3 + 15*q^2 + 25*q + 21 if q%2==0 else 7*q^4 + 17*q^3 + 35*q^2 + 70*q + 99 if q%3==0 else 7*q^4 + 17*q^3 + 35*q^2 + 71*q + 103)
%Y A225936 Cf. A188161, A224790, A225928 - A225938.
%K A225936 nonn
%O A225936 1,1
%A A225936 _Eric M. Schmidt_, May 21 2013