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A237036 Size of the smallest conjugacy class of size greater than 1 of the alternating group of degree n.

%I A237036 #30 Apr 07 2018 07:42:15
%S A237036 3,12,40,70,105,168,240,330,440,572,728,910,1120,1360,1632,1938,2280,
%T A237036 2660,3080,3542,4048,4600,5200,5850,6552,7308,8120,8990,9920,10912,
%U A237036 11968,13090,14280,15540,16872,18278,19760,21320,22960,24682,26488,28380,30360,32430
%N A237036 Size of the smallest conjugacy class of size greater than 1 of the alternating group of degree n.
%H A237036 Wikipedia, <a href="http://en.wikipedia.org/wiki/Alternating_group">Alternating group</a>
%F A237036 From _Alois P. Heinz_, Feb 04 2014: (Start)
%F A237036 G.f.: -x^4*(7*x^8-28*x^7+42*x^6-20*x^5-20*x^4+30*x^3-10*x^2-3)/(x-1)^4.
%F A237036 a(n) = 2*C(n,3) = A007290(n) for n>=9. (End)
%e A237036 For n = 4 the conjugacy classes of size greater than 1 of Alt(n) are
%e A237036 {(1,2)(3,4), (1,3)(2,4), (1,4)(2,3)},
%e A237036 {(2,4,3), (1,2,3), (1,3,4), (1,4,2)},
%e A237036 {(2,3,4), (1,2,4), (1,3,2), (1,4,3)},
%e A237036 the smallest of which has 3 elements, hence a(4) = 3.
%t A237036 Join[{3,12,40,70,105},2*Binomial[Range[9,50],3]] (* _Harvey P. Dale_, Apr 07 2018 *)
%o A237036 (GAP)
%o A237036 a:=function(n)
%o A237036 local G,CC,SCC,SCC1;
%o A237036 G:=AlternatingGroup(n);
%o A237036 CC:=ConjugacyClasses(G);;
%o A237036 SCC:=List(CC,Size);
%o A237036 SCC1:=Difference(SCC,[1]);
%o A237036 return Minimum(SCC1);
%o A237036 end;;
%Y A237036 Cf. A000702, A070733, A007290.
%K A237036 nonn
%O A237036 4,1
%A A237036 _W. Edwin Clark_, Feb 02 2014