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!)
A068393 Number of partitions of n X n checkerboard by two edgewise-connected sets which produce the maximum n^2-2n+2 frontier edges between the two sets. Partitions equal under rotation or reflection are counted only once. 3
2, 3, 7, 44, 494, 748827, 99987552, 23904291912, 23904291912, 14647978829979, 16186345621426754, 45843626565163628751, 235646717730827228414584, 3099290829556018890177304005 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
For even n > 2 the only symmetry possible is rotation by 180 degrees. For odd n > 1 the only symmetries are reflections either horizontally or vertically. - Andrew Howroyd, Apr 15 2016
LINKS
EXAMPLE
From Andrew Howroyd, Apr 15 2016: (Start)
Case n=4: There are 2 nonisomorphic symmetrical solutions (see illustration below). a(4)=(A068381(4)/8 + 2)/2 = 7.
__.__.__.__. __.__.__.__.
| __ __| | __ | |
| | | | | | | | | |
|__| |__| | | | |__| |
|__.__.__.__| |__|__.__.__|
Case n=5: There are 7 nonisomorphic symmetrical solutions (see illustration below). a(5)=(A068381(5)/8 + 7)/2 = 44.
__.__.__.__.__. __.__.__.__.__. __.__.__.__.__. __.__.__.__.__.
| __| |__ | | __| |__ | | |__ __| | | | __ | |
| |__ __| | | | __ | | | __| |__ | | | | | | |
| __| |__ | | | | | | | | | __ | | | | | | | |
| |__.__.__| | | |__| |__| | | |__| |__| | | |__| |__| |
|__.__.__.__.__| |__.__.__.__.__| |__.__.__.__.__| |__.__.__.__.__|
__.__.__.__.__. __.__.__.__.__. __.__.__.__.__.
|__.__ __.__| |__ __ __| | __ __ |
| __| |__ | | | | | | | |__| | | |__|
| | __ | | | | | | | | | __| |__ |
| |__| |__| | | |__| |__| | | |__.__.__| |
|__.__.__.__.__| |__.__.__.__.__| |__.__.__.__.__|
(End)
CROSSREFS
Sequence in context: A267507 A344561 A014546 * A032053 A343522 A086542
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 03 2002
EXTENSIONS
a(7)-a(15) from Andrew Howroyd, Apr 15 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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 25 10:01 EDT 2024. Contains 371967 sequences. (Running on oeis4.)