cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A212319 The number of abstract groups with minimal permutation representations of degree n.

This page as a plain text file.
%I A212319 #20 Oct 27 2013 04:54:15
%S A212319 1,1,2,5,7,13,26,82,104,212,441,1171,1780
%N A212319 The number of abstract groups with minimal permutation representations of degree n.
%C A212319 a(n) can be derived by setting a(1)=1 and then taking the differences between the consecutive elements of A174511. This is due to the fact that if an abstract group can be represented as a permutation group on n points, then it can also be represented by a permutation group of degree n+1, simply by including a fixed point. In other words, the sum of the first n terms give you the number of isomorphism classes of subgroups of the symmetric group of degree n.
%F A212319 a(1)=1, a(n) =  A174511(n) -  A174511(n-1), n>1.
%e A212319 a(1)=1, since only the trivial group 1 can be represented as permutations of a single point. a(2)=1 because Z_2,1 can both be realized by permutations of two points but for 1 this representation is not minimal. a(3)=2 with Z_3 and S_3 appearing for the first time.
%Y A212319 Cf. A174511.
%K A212319 nonn,more
%O A212319 1,3
%A A212319 _Attila Egri-Nagy_, Oct 25 2013