# [seqfan] Re: Occupancy count maps perfect squares

Ron Hardin rhhardin at att.net
Thu Dec 20 14:49:57 CET 2012

Another occupancy perfect square case, counts square-rooted

T(n,k)=Square root of number of nXk arrays of occupancy after each element moves
to some horizontal or vertical neighbor, with every occupancy equal to zero or
two

Table starts
_0__0_0___1__0___0___0___1_0_0
_0__2_0___4__0___8___0__16_0__
_0__0_0___9__0___0___0_105____
_1__4_9__23_57_142_353________
_0__0_0__57__0________________
_0__8_0_142___________________
_0__0_0_______________________
_1_16_________________________
_0____________________________

Some examples for 4X4
..0..2..2..2....0..0..0..2....2..0..2..0....2..0..2..0....2..0..0..2..
..0..2..0..0....2..2..0..2....2..0..2..0....2..0..2..0....2..0..0..2..
..0..2..2..2....2..0..0..2....2..2..2..0....2..0..0..2....2..2..0..0..
..0..2..0..0....2..0..0..2....0..0..2..0....0..0..2..2....0..0..2..2..

..0..0..0..0....2..2..0..0....0..2..0..2....0..2..0..0....2..2..2..0..
..2..2..2..2....0..2..0..2....0..2..0..2....0..2..2..2....0..0..2..0..
..2..2..0..0....0..2..0..2....2..2..0..2....0..0..2..2....2..2..0..2..
..0..0..2..2....0..2..2..0....0..2..0..0....2..2..0..0....0..0..0..2..

..2..2..0..0....0..2..2..0....0..2..2..0....0..0..2..0....0..2..0..2..
..2..0..0..2....2..2..2..2....0..2..0..0....2..0..2..2....0..2..0..2..
..2..0..0..2....0..0..0..0....2..2..2..2....2..0..0..2....2..2..0..2..
..0..0..2..2....0..2..2..0....2..0..0..0....0..2..2..0....0..0..0..2..

rhhardin at mindspring.com
rhhardin at att.net (either)