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!)
A166963 Number of permutations in S_{2n} avoiding 123 and 1432 whose matrices are 180-degree symmetric. 1
1, 2, 6, 12, 27, 61, 138, 309, 694, 1560, 3506, 7877, 17699, 39770, 89363, 200796, 451184, 1013802, 2277993, 5118603, 11501396, 25843403, 58069600, 130481206, 293188608, 658788823, 1480285049 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Trivially, this also counts 180-degree symmetric permutations avoiding 321 and 4123, 123 and 3214, or 321 and 2341. For the other 140 pairs of patterns in S_3 and S_4, the sequence of symmetric permutations avoiding those patterns is either finite (as in 123 and 4321, by Erdos-Szekeres) or counted by an easily-recognized sequence such as alternating Fibonacci numbers, Catalan numbers, squares plus one, or the naturals.
LINKS
FORMULA
a(n) = 2a(n-1) + a(n-3) + a(n-4) - a(n-5).
G.f.: (-x^3 + 2x^2 + 1)/(x^5 - x^4 - x^3 - 2x + 1).
EXAMPLE
For n=2, the a(2) = 6 solutions are 2143, 2413, 3142, 3412, 4231, and 4321. The two other 180-degree symmetric permutations in S_4 are 1234 and 1324, both of which contain the pattern 123.
MATHEMATICA
LinearRecurrence[{2, 0, 1, 1, -1}, {1, 2, 6, 12, 27}, 50] (* G. C. Greubel, May 29 2016 *)
CROSSREFS
Sequence in context: A059078 A335712 A356465 * A188476 A155583 A140853
KEYWORD
nonn
AUTHOR
David Lonoff and Jonah Ostroff (jonah.ostroff(AT)gmail.com), Oct 25 2009
EXTENSIONS
Fixed typos caused by non-ASCII symbol Jonah Ostroff (jonah.ostroff(AT)gmail.com), Oct 25 2009
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 28 01:34 EDT 2024. Contains 372900 sequences. (Running on oeis4.)