OFFSET
0,3
COMMENTS
a(n) is the number of rearrangement patterns, i.e., the number of rearrangement map equivalence classes.
REFERENCES
J. Burns, Counting a Class of Signed Permutations and Chord Diagrams related to DNA Rearrangement, Preprint.
LINKS
FORMULA
a(n)=2^(n-2)*(n!+floor(n/2)!)
a(n)~(pi*n/8)^(1/2) (2n/e)^n
EXAMPLE
For n=1 the a(1)=1 solution is the equivalence class {+1,-1}.For n=2 the a(2)=3 solutions are the equivalence classes {+1+2, -2-1}, {+1-2, +2-1, -2+1, -1+2}, and {+2+1, -1-2}
MATHEMATICA
Table[2^(n-2)*(n!+Floor[n/2]!), {n, 10}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jonathan Burns, Apr 02 2016
STATUS
approved