

A212319


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


0



1, 1, 2, 5, 7, 13, 26, 82, 104, 212, 441, 1171, 1780
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OFFSET

1,3


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..13.


FORMULA

a(1)=1, a(n) = A174511(n)  A174511(n1), n>1.


EXAMPLE

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.


CROSSREFS

Cf. A174511.
Sequence in context: A155028 A119839 A107057 * A161379 A250173 A038945
Adjacent sequences: A212316 A212317 A212318 * A212320 A212321 A212322


KEYWORD

nonn,more


AUTHOR

Attila EgriNagy, Oct 25 2013


STATUS

approved



