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A199574
The number of simple labeled graphs on n nodes where two such graphs are considered equivalent iff one can be obtained from the other by reversing the labeling.
1
1, 2, 6, 40, 544, 16640, 1050624, 134250496, 34360262656, 17592202821632, 18014399046352896, 36893488181778841600, 151115727454027670093824, 1237940039285661749875834880, 20282409603651706452744270249984
OFFSET
1,2
COMMENTS
Equivalently, The number of orbits in the set of simple labeled graphs on n nodes under the action of the permutation group G = {{1,2,...,n},{n,n-1,...,1}}.
The induced group has cycle index= 1/2(s_1^binomial(n,2)+s_1^floor(n/2)s_2^((binomial(n,2)-floor(n/2))/2))
FORMULA
a(n)= (2^floor(n/2)+2^((binomial(n,2)+floor(n/2)/2))/2
EXAMPLE
a(3)=6 because:1-2 3 is equivalent to 1 2-3 and 3-1-2 is equivalent to 1-3-2 while the other four graphs are fixed for a total of 6 orbits.
MATHEMATICA
Table[PairGroupIndex[{e=IdentityPermutation[n], Reverse[e]}, s]/.Table[s[i]->2, {i, 1, 2}], {n, 1, 20}]
CROSSREFS
Sequence in context: A133939 A045846 A238818 * A379695 A320489 A135755
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Nov 09 2011
STATUS
approved