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T(n,k)=Number of nXk 0..3 arrays with values 0..3 introduced in row major order, the number of instances of each value within one of each other, and every element equal to two or fewer horizontal or vertical neighbors
8

%I #9 May 06 2020 01:59:07

%S 1,1,1,1,1,1,1,45,45,1,10,105,1260,105,10,45,6300,15400,15400,6300,45,

%T 105,15400,2513869,2491383,2513869,15400,105,105,1030230,174524175,

%U 425836476,425836476,174524175,1030230,105,1260,2559433,5866391058

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

%C Table starts

%C ....1.........1...........1..............1...............10...............45

%C ....1.........1..........45............105.............6300............15400

%C ....1........45........1260..........15400..........2513869........174524175

%C ....1.......105.......15400........2491383........425836476......76066541392

%C ...10......6300.....2513869......425836476....1036302685728.1049206835165446

%C ...45.....15400...174524175....76066541392.1049206835165446

%C ..105...1030230..5866391058.14045226977086

%C ..105...2559433.78538951349

%C .1260.182663916

%C .6300

%H R. H. Hardin, <a href="/A199523/b199523.txt">Table of n, a(n) for n = 1..60</a>

%e Some solutions for n=4 k=3

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

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

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

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

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Nov 07 2011