

A358289


Generalized Gerrymander sequence: number of ordered ways to divide an n X n square into two connected regions, both of area n^2/2 if n is even, or of areas (n^21)/2 and (n^2+1)/2 if n is odd.


3



0, 4, 16, 140, 2804, 161036, 27803749, 14314228378, 21838347160809, 99704315229167288, 1367135978051264146578, 56578717186086829451888706, 7065692298178203128922479762418, 2670113158846160742372913777087464324, 3052313665715695874527667027409186333152556
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS



FORMULA



EXAMPLE

For n = 2, the square can be split vertically or horizontally, and then there are two ways to order the regions, so a(2) = 2*2 = 4.
For n = 3 we must choose a connected region of area 4 with a connected complement of area 5.
The possibilities are
XXO XXX XXX
XXO XOO OXO
OOO OOO OOO
4 ways 8 ways 4 ways
so a(3) = 16.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



