A378279 - OEIS

%I #12 Nov 27 2024 12:33:36

%S 0,0,1,4,20,160,910,5936,53424,397440,3304620,35023120,322852816

%N Number of subgroups of S_n isomorphic to S_3, where S_n is the n-th symmetric group.

%F a(n) = (A281097(n) - A000085(n))/6. See A378163 for more information.

%o (GAP) A378279 := function(n)

%o local S;

%o S := SymmetricGroup(n);

%o return Sum(IsomorphicSubgroups(S, SymmetricGroup(3)), x->Index(S, Normalizer(S, Image(x))));

%o end;

%Y Column k=3 of A378163.

%Y Cf. A000085, A378280, A378281, A281097.

%K nonn,hard,more

%O 1,4

%A _Jianing Song_, Nov 21 2024