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
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Nov 09 2011
STATUS
approved