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%I #13 Jun 28 2017 00:59:38
%S 0,1,1,2,9,2,4,49,49,4,8,289,656,289,8,16,1681,12544,12544,1681,16,32,
%T 9801,200072,643204,200072,9801,32,64,57121,3485689,31203396,31203396,
%U 3485689,57121,64,128,332929,58132316,1539699121,4235650596,1539699121
%N T(n,k) = number of n X k arrays of occupancy after each element moves to some horizontal or vertical neighbor, with no occupancy greater than 2.
%C Table starts
%C ....0........1............2...............4.................8
%C ....1........9...........49.............289..............1681
%C ....2.......49..........656...........12544............200072
%C ....4......289........12544..........643204..........31203396
%C ....8.....1681.......200072........31203396........4235650596
%C ...16.....9801......3485689......1539699121......619901126244
%C ...32....57121.....58132316.....75512292025....86907967843320
%C ...64...332929....990486784...3709710975721.12474883501876324
%C ..128..1940449..16699002692.182118668668225
%C ..256.11309769.282999528529
%C ..512.65918161
%C .1024
%C Even rows and columns are perfect squares.
%H R. H. Hardin, <a href="/A221139/b221139.txt">Table of n, a(n) for n = 1..84</a>
%e Some solutions for n=3, k=4:
%e ..1..1..1..2....1..1..1..1....1..1..0..2....1..1..2..1....1..1..2..0
%e ..2..1..0..1....0..0..1..0....2..2..1..1....1..2..0..1....1..1..0..0
%e ..0..1..2..0....2..2..2..1....0..0..2..0....0..2..0..1....1..2..1..2
%Y Column 1 is A000079(n-2).
%Y Column 2 is A090390.
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Jan 02 2013
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