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!)
A081623 Number of ways in which the points on an n X n square lattice can be equally occupied with spin "up" and spin "down" particles. If n is odd, we arbitrarily take the lattice to contain one more spin "up" particle than the number of spin "down" particles. 1
1, 1, 6, 126, 12870, 5200300, 9075135300, 63205303218876, 1832624140942590534, 212392290424395860814420, 100891344545564193334812497256, 191645966716130525165099506263706416, 1480212998448786189993816895482588794876100 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Brian Hayes, The World in a Spin, American Scientist 88:5 (September-October 2000), pp. 384-388. [alternate link]
FORMULA
a(n) = C(n^2, (n^2+1)/2) if n is odd and C(n^2, n^2/2) if n is even.
a(n) = binomial(n^2,floor(n^2/2)). - Alois P. Heinz, Jul 21 2017
EXAMPLE
a(2) = C(4,2) = 6.
a(3) = C(9,5) = 126.
MAPLE
a:= n-> (s-> binomial(s, floor(s/2)))(n^2):
seq(a(n), n=0..15); # Alois P. Heinz, Jul 21 2017
PROG
(Mathcad or Microsoft Excel): f(n)=combin(n^2, trunc((n^2+1)/2))
(PARI) a(n)=binomial(n^2, n^2\2) \\ Charles R Greathouse IV, May 09 2013
CROSSREFS
A082963 is the equivalent sequence up to reflection and rotation.
Sequence in context: A237428 A255900 A133792 * A223210 A324093 A177756
KEYWORD
easy,nonn
AUTHOR
A. Timothy Royappa, Apr 22 2003
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Jul 21 2017
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 March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)