|
|
A271216
|
|
a(n) = 2^n floor(n/2)!
|
|
2
|
|
|
1, 2, 4, 8, 32, 64, 384, 768, 6144, 12288, 122880, 245760, 2949120, 5898240, 82575360, 165150720, 2642411520, 5284823040, 95126814720, 190253629440, 3805072588800
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Number of symmetric rearrangement maps, i.e., rearrangement maps which satisfy a=a^(AI) and a^A = a^I.
|
|
REFERENCES
|
J. Burns, Counting a Class of Signed Permutations and Chord Diagrams related to DNA Rearrangement, Preprint.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2^n floor(n/2)!
|
|
EXAMPLE
|
For n=0 the a(0)=1 solution is { ∅ }
For n=1 the a(1)=2 solutions are { +1, -1 }
For n=2 the a(2)=4 solutions are { +1+2, -2-1, +2+1, -1-2 }
For n=3 the a(3)=8 solutions are { +1+2+3, -3-2-1, +3-2+1, -1+2-3, +3+2+1, -1-2-3, +1-2+3, -3+2-1 }
|
|
MATHEMATICA
|
Table[2^n*Floor[n/2]!, {n, 0, 20}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|