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.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A271217 Number of symmetric reduced rearrangement maps. 3
 1, 2, 2, 6, 22, 50, 274, 598, 4486, 9570, 90914, 191398, 2201078, 4593554, 62012978, 128619510, 1993602406, 4115824322, 72026925634, 148169675590, 2889308674006 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is the number of reduced rearrangement maps on n blocks. A rearrangement map is a signed permutation, e.g., +2 -1 -3. If the permutation contains (i)(i+1) or -(i+1)-(i) for any i, then it is not reduced. The map a is symmetric if a=a^(AI) and a^A = a^I where A and I are the rotation involutions. REFERENCES J. Burns, Counting a Class of Signed Permutations and Chord Diagrams related to DNA Rearrangement, Preprint. LINKS Table of n, a(n) for n=0..20. J. Burns, Table of Rearrangement Maps and Patterns for n = 1, 2, and 3. FORMULA a(n) = round( 2^n * e^(-1/4) * ( 1 - (1 + (-1)^n)/(4n) ) * floor(n/2)! ) a(2k+1) = 2*a(2k) + a(2k-1) and a(2k) = (2k-1)*a(2k-1)+(2k-2)*a(2k-3) a(n) ~ e^(-1/4) * 2^n * floor(n/2)!. Conjecture: (-2*n+9)*a(n) -4*a(n-1) +(2*n-3)*(2*n-7)*a(n-2) -4*a(n-3) +2*(2*n-5)*(n-4)*a(n-4)=0. - R. J. Mathar, Jan 04 2017 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)=2 solutions are { +2+1, -1-2 } For n=3 the a(3)=6 solutions are { +3-2+1, -1+2-3, +3+2+1, -1-2-3, +1-2+3, -3+2-1 } MATHEMATICA Table[Round[2^n*Exp[-1/4]*(1-(1+(-1)^n)/(4 n))*Floor[n/2]!], {n, 1, 20}] CROSSREFS A271217 / A271216 ~ e^(-1/4). Cf. A271212, A271214 Sequence in context: A320932 A225942 A004077 * A202743 A007985 A097090 Adjacent sequences: A271214 A271215 A271216 * A271218 A271219 A271220 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.

Last modified May 21 19:35 EDT 2024. Contains 372738 sequences. (Running on oeis4.)