A225930 Number of conjugacy classes in twisted Chevalley group 3D4(q) as q runs through the prime powers.

35, 126, 345, 786, 2806, 4685, 7386, 16110, 30946, 69909, 88746, 137566, 292566, 406906, 551886, 732546, 954310, 1082405, 1926226, 2896410, 3500206, 4985766, 5884906, 8042226, 12326286, 14076610, 17043525, 20456446, 25774710, 28792666, 39449446, 43584810, 48037086

Offset: 1

Author

Eric M. Schmidt, May 21 2013

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Eric M. Schmidt)
• Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.

Crossrefs

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

Programs

Mathematica

Map[(#^2 + 1)*(# + 1)*# + 5 + Mod[#, 2] &, Select[Range[100], PrimePowerQ]] (* Paolo Xausa, Jan 16 2025 *)

PARI

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

Formula

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.