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T(n,k)=Number of nXk 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors
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%I #5 Mar 31 2012 12:36:35

%S 0,1,1,1,3,1,2,13,13,2,3,65,132,65,3,6,393,2453,2453,393,6,11,2539,

%T 42420,125468,42420,2539,11,23,16866,794416,6235011,6235011,794416,

%U 16866,23,47,113432,14511531,316561994,839006010,316561994,14511531,113432,47,102

%N T(n,k)=Number of nXk 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors

%C Table starts

%C ...0.......1...........1..............2................3.................6

%C ...1.......3..........13.............65..............393..............2539

%C ...1......13.........132...........2453............42420............794416

%C ...2......65........2453.........125468..........6235011.........316561994

%C ...3.....393.......42420........6235011........839006010......117380324984

%C ...6....2539......794416......316561994.....117380324984....44832664800117

%C ..11...16866....14511531....15958823113...16158623337745.16925667317073175

%C ..23..113432...268456338...806680624447.2239304268913257

%C ..47..766473..4940928443.40736752748774

%C .102.5188597.91146218920

%H R. H. Hardin, <a href="/A199149/b199149.txt">Table of n, a(n) for n = 1..83</a>

%e Some solutions for n=3 k=3

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_ Nov 03 2011