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

1,1

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

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.

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 *)

Prog

(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)

Crossrefs

Cf. A188161, A224790, A225928-A225937.

Sequence in context: A321245 A157168 A062915 * A221813 A232004 A034979

Adjacent sequences: A225935 A225936 A225937 * A225939 A225940 A225941

Keyword

nonn

Author

Eric M. Schmidt, May 21 2013

Status

approved