A271217 -id:A271217 - cp's OEIS frontend

A271214 Number of reduced rearrangement patterns with n blocks.

1, 1, 2, 10, 71, 653, 7638, 104958, 1664083, 29740057, 591645738, 12959409010, 309898317151, 8032551265957, 224316415082750, 6714021923017318, 214415538303362411, 7277133405318569009, 261560966377901961810, 9925178291099012783322, 396498148141095399675511

Offset: 0

Jonathan Burns, Apr 13 2016

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.

			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 }

J. Burns, Counting a Class of Signed Permutations and Chord Diagrams related to DNA Rearrangement, Preprint.

G. C. Greubel, Table of n, a(n) for n = 0..400
J. Burns, Table of Rearrangement Maps and Patterns for n = 1, 2, and 3.

Cf. A271212, A271217.

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}]

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.

A271213 a(n) = 2^(n-2) * (n! + floor(n/2)!).

Original entry on oeis.org

1, 1, 3, 14, 104, 976, 11616, 161472, 2582016, 46451712, 929003520, 20437463040, 490498375680, 12752940072960, 357082301399040, 10712468463943680, 342798990185594880, 11655165645170933760, 419585963202371911680, 15944266600833991311360, 637770664032408384307200

Offset: 0

Jonathan Burns, Apr 02 2016

a(n) is the number of rearrangement patterns, i.e., the number of rearrangement map equivalence classes.

			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}

J. Burns, Counting a Class of Signed Permutations and Chord Diagrams related to DNA Rearrangement, Preprint.

J. Burns, Table of Rearrangement Maps and Patterns for n = 1, 2, and 3.

Partition of A000165 into equivalence classes.

Cf. A271214, A271216, A271217.

Mathematica
```
Table[2^(n-2)*(n!+Floor[n/2]!),{n,10}]
```

a(n)=2^(n-2)*(n!+floor(n/2)!)

a(n)~(pi*n/8)^(1/2) (2n/e)^n

cp's OEIS Frontend

A271214 Number of reduced rearrangement patterns with n blocks.

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