A225937 Number of conjugacy classes in adjoint Chevalley group E_7(q) as q runs through the prime powers.
531, 4569, 24553, 105644, 992834, 2447517, 5477205, 21674822, 68494004, 287617189, 437805224, 946620206, 3567305234, 6369359984, 10879403385, 17889596996, 28462405562, 35505127221, 97646355404, 199751157632, 278452165094, 517886829194, 692659723976
Offset: 1
Keywords
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.
Programs
-
Sage
def A225937(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 5*q^4 + 13*q^3 + 24*q^2 + 46*q + 57 if q%3==0 else 5*q^4 + 13*q^3 + 24*q^2 + 47*q + 59)
Formula
Let q be the n-th prime power. Then, a(n) is
q^7 + q^6 + 2q^5 + 4q^4 + 10q^3 + 15q^2 + 25q + 21 if q == 0 (mod 2);
q^7 + q^6 + 2q^5 + 5q^4 + 13q^3 + 24q^2 + 46q + 57 if q == 0 (mod 3);
q^7 + q^6 + 2q^5 + 5q^4 + 13q^3 + 24q^2 + 47q + 59 otherwise.