The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A271214 Number of reduced rearrangement patterns with n blocks. 3
1, 1, 2, 10, 71, 653, 7638, 104958, 1664083, 29740057, 591645738, 12959409010, 309898317151, 8032551265957, 224316415082750, 6714021923017318, 214415538303362411, 7277133405318569009, 261560966377901961810, 9925178291099012783322, 396498148141095399675511 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
a(n) is the number of reduced rearrangement patterns, i.e., the number of reduced rearrangement map equivalence classes formed from the two rotation involutions.
REFERENCES
J. Burns, Counting a Class of Signed Permutations and Chord Diagrams related to DNA Rearrangement, Preprint.
LINKS
FORMULA
a(n) = ( round( 2^n e^(-1/2) (n+1/2) (n-1)! ) + round( 2^n e^(-1/4) (1-(1+(-1)^n)/4n)) floor(n/2)! ) / 4.
a(n) ~ sqrt( Pi*n / 8*e) * (2n / e)^n.
a(n) = (A271212(n) + A271217(n)) / 4.
EXAMPLE
For n=0 the a(0)=1 solution is { ∅ }
For n=1 the a(1)=1 solution is { +1 }
For n=2 the a(2)=2 solutions are { +2+1, +1-2 }
For n=3 the a(3)=10 solutions are { +3-2+1, +1+3-2, +2-3+1, +1+3+2, +2+1-3, +3+1-2, +1-3+2, +3+2+1, +3+2-1, +1-2+3 }
MATHEMATICA
Table[(Round[2^n*Exp[-1/2]*(n + 1/2)*(n - 1)!] + Round[2^n*Exp[ -1/4]*(1 - (1 + (-1)^n)/(4 n))*Floor[n/2]!])/4, {n, 1, 20}]
CROSSREFS
Sequence in context: A362821 A060842 A245834 * A366241 A321446 A111554
KEYWORD
nonn,easy
AUTHOR
Jonathan Burns, Apr 13 2016
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 03:12 EDT 2024. Contains 372617 sequences. (Running on oeis4.)