

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
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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



FORMULA

a(n) = round( 2^n * e^(1/4) * ( 1  (1 + (1)^n)/(4n) ) * floor(n/2)! )
a(2k+1) = 2*a(2k) + a(2k1) and a(2k) = (2k1)*a(2k1)+(2k2)*a(2k3)
a(n) ~ e^(1/4) * 2^n * floor(n/2)!.
Conjecture: (2*n+9)*a(n) 4*a(n1) +(2*n3)*(2*n7)*a(n2) 4*a(n3) +2*(2*n5)*(n4)*a(n4)=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, 12 }
For n=3 the a(3)=6 solutions are { +32+1, 1+23, +3+2+1, 123, +12+3, 3+21 }


MATHEMATICA

Table[Round[2^n*Exp[1/4]*(1(1+(1)^n)/(4 n))*Floor[n/2]!], {n, 1, 20}]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



