来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a049314 Showing 1-1 of 1 %I A049314 %S A049314 1,3,15,60,252,1005,4080,16305,65460,261828,1048260,4192980,16775955, %T A049314 67103520,268430160,1073720415,4294945932,17179782540,68719391100, %U A049314 274877559420,1099511281260,4398045120300,17592184654365,70368738597600,281474971147680 %N A049314 The number k(GL(n,q)) of conjugacy classes in GL(n,q), q=4. %C A049314 Bound: k(GL(n,q))n,a(n)n=0…500的表%H A049 314 W. Feit和N. J. Fine,有限域上的交换矩阵对Duke Math。Journal,27(1960)91-94.0%F A049 314,GL(n,q)中共轭类的数量A(n)是无限乘积中T^ n的系数:乘积K=1, 2,…(1-t^ k)/(1-qt^ k)- Noam Katz(NOAMKJ(AT)Hotmail。com),3月30日2001。F %A049 314 G.F.:EXP(SUMU{{K>=1 }(SuMu{{K} k* D*(4 ^(k/d)-1))*x^ k/k)。- _Ilya Gutkovskiy_, Sep 27 2018 %p A049314 with(numtheory): %p A049314 b:= proc(n) b(n):= add(phi(d)*4^(n/d), d=divisors(n))/n-1 end: %p A049314 a:= proc(n) a(n):= `if`(n=0, 1, %p A049314 add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n) %p A049314 end: %p A049314 seq(a(n), n=0..30); # _Alois P. Heinz_, Nov 03 2012 %t A049314 b[n_] := Sum[EulerPhi[d]*4^(n/d), {d, Divisors[n]}]/n-1; a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*b[d], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Jan 24 2014, after _Alois P. Heinz_ *) %o A049314 (MAGMA)/* The program does not work for n>9: */ [1] cat [NumberOfClasses(GL(n,4)) : n in [1..8]]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006; edited by _Vincenzo Librandi_, Jan 23 2013 %o A049314 (PARI) x='x+O('x^30); Vec(prod(n=1, 30, (1-x^n)/(1-4*x^n))) \\ _Altug Alkan_, Sep 27 2018 %Y A049314 Cf. A006951, A006952, A049315, A049316. %K A049314 nonn %O A049314 0,在OEIS最终用户许可协议下,A04314-VLADETA JoVoViviz的内容为2(%),即:HTTP:/OEIS.Org/许可证。