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T(n,k)=Number of nXk 0..3 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..3 order
7

%I #4 Feb 21 2013 13:55:48

%S 1,1,1,1,1,1,4,1,1,4,5,10,5,10,5,14,11,42,42,11,14,17,126,45,235,45,

%T 126,17,75,139,1582,1450,1450,1582,139,75,95,2033,2953,30883,11994,

%U 30883,2953,2033,95,411,2229,104833,267772,574388,574388,267772,104833,2229

%N T(n,k)=Number of nXk 0..3 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..3 order

%C Table starts

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

%C ....1......1.........1...........10..............11..............126

%C ....1......1.........5...........42..............45.............1582

%C ....4.....10........42..........235............1450............30883

%C ....5.....11........45.........1450...........11994...........574388

%C ...14....126......1582........30883..........574388.........18213127

%C ...17....139......2953.......267772.........4927416........544804117

%C ...75...2033....104833......7073732.......482530769......39402895960

%C ...95...2229....179105.....67911068......4741171798....1636155043302

%C ..411..36255...6910335...1835377464....481046300094..146686792732538

%C ..519..39685..12297363..17762404598...4838816683797.6439927626021526

%C .2522.667198.463356818.478005487727.496656128182183

%H R. H. Hardin, <a href="/A222479/b222479.txt">Table of n, a(n) for n = 1..143</a>

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A222372

%K nonn,tabl

%O 1,7

%A _R. H. Hardin_ Feb 21 2013