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T(n,k)=Number of 2nX2k 0..4 arrays with values 0..4 introduced in row major order and each element equal to an even number of horizontal and vertical neighbors.
4

%I #11 Feb 04 2023 05:30:44

%S 5,404,404,67442,7937268,67442,11739910,163506788110,163506788110,

%T 11739910,2048681430,3368739754955320,397739142470871040,

%U 3368739754955320,2048681430,357559607382,69406373651979823710

%N T(n,k)=Number of 2nX2k 0..4 arrays with values 0..4 introduced in row major order and each element equal to an even number of horizontal and vertical neighbors.

%C Table starts

%C ............5..................404....................67442

%C ..........404..............7937268.............163506788110

%C ........67442.........163506788110.......397739142470871040

%C .....11739910.....3368739754955320.967523967174230258261646

%C ...2048681430.69406373651979823710

%C .357559607382

%H R. H. Hardin, <a href="/A198538/b198538.txt">Table of n, a(n) for n = 1..24</a>

%e Some solutions for n=3 k=2

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

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

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

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

%e ..0..4..0..0....1..0..2..2....1..0..2..2....3..4..0..4....1..0..3..0

%e ..3..1..0..0....0..4..3..1....2..1..0..4....2..0..4..0....2..1..0..3

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Oct 26 2011