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T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, without move-in move-out left turns
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%I #4 Jan 21 2013 11:39:26

%S 0,1,0,2,4,0,4,24,12,0,8,165,230,40,0,16,1054,5879,2594,136,0,32,6862,

%T 128076,233781,28478,460,0,64,44576,2853634,17254611,9205038,313721,

%U 1556,0,128,289789,63318470,1312503181,2299842566,361920243,3449644,5264,0

%N T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, without move-in move-out left turns

%C Table starts

%C .0....1.......2.........4..........8.........16..........32.........64.....128

%C .0....4......24.......165.......1054.......6862.......44576.....289789.1883406

%C .0...12.....230......5879.....128076....2853634....63318470.1408047450

%C .0...40....2594....233781...17254611.1312503181.99007036296

%C .0..136...28478...9205038.2299842566

%C .0..460..313721.361920243

%C .0.1556.3449644

%C .0.5264

%C .0

%H R. H. Hardin, <a href="/A221655/b221655.txt">Table of n, a(n) for n = 1..49</a>

%e Some solutions for n=3 k=4

%e ..0..0..2..1....0..1..3..1....0..1..0..1....0..2..0..1....0..2..2..1

%e ..1..4..2..0....0..1..1..2....0..3..3..1....2..0..1..1....1..0..0..1

%e ..0..0..1..1....1..1..1..0....1..0..2..0....0..2..3..0....1..2..2..0

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Jan 21 2013