A225938 Number of conjugacy classes in Chevalley group E_8(q) as q runs through the prime powers (A246655).

1156, 12825, 97154, 519071, 6906102, 19543486, 49150839, 238045722, 889575240, 4600759094, 7439557452, 17980383618, 82034207430, 159213167411, 293713437009, 518754968088, 882274298862, 1136129443366, 3612770425152, 8189556710532, 11973138177210, 24340206797502

Offset: 1

Author

Eric M. Schmidt, May 21 2013

Keywords

• nonn

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..1000
• Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.
• Index entries for sequences related to groups

Crossrefs

Cf. A188161, A224790, A225928-A225937.

Programs

Maple

A225938 := proc(n)
    local q ;
    q := A246655(n) ;
    if modp(q,2) = 0 then
        q^8 + q^7 + 2*q^6 + 3*q^5 +  9*q^4 + 14*q^3 + 32*q^2 + 47*q +  70;
    elif modp(q,3) = 0 then
        q^8 + q^7 + 2*q^6 + 3*q^5 + 10*q^4 + 16*q^3 + 39*q^2 + 65*q + 102 ;
    elif modp(q,5) = 0 then
        q^8 + q^7 + 2*q^6 + 3*q^5 + 10*q^4 + 16*q^3 + 40*q^2 + 67*q + 111 ;
    else
        q^8 + q^7 + 2*q^6 + 3*q^5 + 10*q^4 + 16*q^3 + 40*q^2 + 67*q + 112 ;
    end if;
end proc: # R. J. Mathar, Jan 09 2017

Mathematica

qmax = 100;
Reap[For[q = 2, q < qmax, q++, If[PrimePowerQ[q], cc = q^8 + q^7 + 2 q^6 + 3 q^5 + Which[Mod[q, 2] == 0, 9 q^4 + 14 q^3 + 32 q^2 + 47 q + 70, Mod[q, 3] == 0, 10 q^4 + 16 q^3 + 39 q^2 + 65 q + 102, Mod[q, 5] == 0, 10 q^4 + 16 q^3 + 40 q^2 + 67 q + 111, True, 10 q^4 + 16 q^3 + 40 q^2 + 67 q + 112]; Sow[cc]]]][[2, 1]] (* Jean-François Alcover, Mar 24 2020 *)

Sage

def A225938(q) : return q^8 + q^7 + 2*q^6 + 3*q^5 + (9*q^4 + 14*q^3 + 32*q^2 + 47*q + 70 if q%2==0 else 10*q^4 + 16*q^3 + 39*q^2 + 65*q + 102 if q%3==0 else 10*q^4 + 16*q^3 + 40*q^2 + 67*q + 111 if q%5==0 else 10*q^4 + 16*q^3 + 40*q^2 + 67*q + 112)

Formula

Let q be the n-th prime power. Then a(n) is

q^8 + q^7 + 2q^6 + 3q^5 + 9q^4 + 14q^3 + 32q^2 + 47q + 70, q==0(mod 2);

q^8 + q^7 + 2q^6 + 3q^5 + 10q^4 + 16q^3 + 39q^2 + 65q + 102, q==0(mod 3);

q^8 + q^7 + 2q^6 + 3q^5 + 10q^4 + 16q^3 + 40q^2 + 67q + 111, q==0(mod 5);

q^8 + q^7 + 2q^6 + 3q^5 + 10q^4 + 16q^3 + 40q^2 + 67q + 112, otherwise.