|
| |
|
|
A061714
|
|
Number of types of (n-1)-swap moves for traveling salesman problem. Number of circular permutations on elements 0,1,...,2n-1 where every two elements 2i,2i+1 and no two elements 2i-1,2i are adjacent.
|
|
4
| |
|
|
1, 0, 1, 4, 25, 208, 2121, 25828, 365457, 5895104, 106794993, 2147006948, 47436635753, 1142570789072, 29797622256377, 836527783016196, 25153234375160993, 806519154686509056, 27470342073410272609
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
COMMENTS
| An n-swap move consists of the removal of n edges and addition of n different edges which result in a new tour. The type can be characterized by how the n segments of the original tour formed by the removal are reassembled.
|
|
|
LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,100
|
|
|
FORMULA
| a(n) = (-1)^n + Sum_{i=0..n-1} (-1)^(n-1-i)*C(n,i+1)*i!*2^i = (-1)^n + A120765(n)
E.g.f.: exp(-x)*(1-log(1-2*x)/2)
|
|
|
MATHEMATICA
| m = 18; CoefficientList[ Series[ Exp[-x]*(1 - Log[1-2x]/2), {x, 0, m}], x]*Range[0, m]! (* From Jean-François Alcover, Jul 25 2011, after g.f. *)
|
|
|
PROG
| (PARI) { for (n=0, 100, a=(-1)^n + sum(i=0, n-1, (-1)^(n-1-i)*binomial(n, i+1)*i!*2^i); write("b061714.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 26 2009]
|
|
|
CROSSREFS
| Cf. A001171 (sequential n-swap moves).
Sequence in context: A088159 A036242 A120955 * A005411 A105628 A203219
Adjacent sequences: A061711 A061712 A061713 * A061715 A061716 A061717
|
|
|
KEYWORD
| nonn,nice
|
|
|
AUTHOR
| David Applegate (david(AT)research.att.com), Jun 21 2001
|
|
|
EXTENSIONS
| Revised by Max Alekseyev (maxale(AT)gmail.com), Jul 03 2006
|
| |
|
|
