|
|
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
|
|
|
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.
|
|
EXAMPLE
|
a(2) = C(4,2) = 6.
a(3) = C(9,5) = 126.
|
|
MAPLE
|
a:= n-> (s-> binomial(s, floor(s/2)))(n^2):
|
|
PROG
|
(Mathcad or Microsoft Excel): f(n)=combin(n^2, trunc((n^2+1)/2))
|
|
CROSSREFS
|
A082963 is the equivalent sequence up to reflection and rotation.
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|