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T(n,k)=Number of nXk 0..2 arrays with no more than floor(nXk/2) elements unequal to at least one horizontal or antidiagonal neighbor, with new values introduced in row major 0..2 order
14

%I #4 Mar 11 2013 06:24:03

%S 1,1,2,1,4,5,4,7,14,14,5,25,43,70,41,14,86,314,584,326,122,17,332,946,

%T 4572,2903,1630,365,70,1172,10417,42607,68385,45718,8058,1094,89,4566,

%U 36987,414907,601407,1037326,227569,40598,3281,326,16562,431995,4405097

%N T(n,k)=Number of nXk 0..2 arrays with no more than floor(nXk/2) elements unequal to at least one horizontal or antidiagonal neighbor, with new values introduced in row major 0..2 order

%C Table starts

%C .....1........1...........1..............4.................5

%C .....2........4...........7.............25................86

%C .....5.......14..........43............314...............946

%C ....14.......70.........584...........4572.............42607

%C ....41......326........2903..........68385............601407

%C ...122.....1630.......45718........1037326..........29158784

%C ...365.....8058......227569.......15904038.........433151066

%C ..1094....40598.....3706702......245900395.......21273422658

%C ..3281...204914....18721501.....3827698634......321537852228

%C ..9842..1041934...309335666....59908716776....15962124223493

%C .29525..5315674..1578160193...941887270541...243618393075038

%C .88574.27228710.26302908158.14864346253334.12191944518185381

%H R. H. Hardin, <a href="/A222986/b222986.txt">Table of n, a(n) for n = 1..159</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A007051(n-1)

%Y Row 1 is A222364

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_ Mar 11 2013