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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 king-move neighbor, with new values introduced in row major 0..2 order
9

%I #4 Feb 17 2013 06:07:19

%S 1,1,1,1,1,1,4,1,1,4,5,10,5,10,5,14,11,40,40,11,14,17,104,43,191,43,

%T 104,17,70,116,858,992,992,858,116,70,89,1126,1801,11249,6214,11249,

%U 1801,1126,89,326,1256,27718,73499,130562,130562,73499,27718,1256,326,413

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

%C Table starts

%C ....1......1........1..........4.............5.............14.............17

%C ....1......1........1.........10............11............104............116

%C ....1......1........5.........40............43............858...........1801

%C ....4.....10.......40........191...........992..........11249..........73499

%C ....5.....11.......43........992..........6214.........130562.........840059

%C ...14....104......858......11249........130562........2372459.......40861043

%C ...17....116.....1801......73499........840059.......40861043......749968281

%C ...70...1126....27718.....860209......27732900.....1104464320....46207222774

%C ...89...1256....50589....6307306.....206541839....24442060020..1021894455344

%C ..326..12524...808582...74012176....6709654616...740497034033.80312827691631

%C ..413..14012..1611649..548361088...51859721195.17490369316698

%C .1630.140410.24401454.6378096812.1709263568642

%H R. H. Hardin, <a href="/A222371/b222371.txt">Table of n, a(n) for n = 1..144</a>

%e Some solutions for n=4 k=4

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

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

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

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

%K nonn,tabl

%O 1,7

%A _R. H. Hardin_ Feb 17 2013