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T(n,k)=Number of 2nX2k 0..2 arrays with values 0..2 introduced in row major order and each element equal to an even number of horizontal and vertical neighbors
5

%I #5 Mar 31 2012 12:36:34

%S 4,36,36,376,2436,376,3936,162776,162776,3936,41216,10937316,70145916,

%T 10937316,41216,431616,734979136,30189380016,30189380016,734979136,

%U 431616,4519936,49393306556,13004327687556,83436203795656,13004327687556

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

%C Table starts

%C ........4............36..............376...............3936..............41216

%C .......36..........2436...........162776...........10937316..........734979136

%C ......376........162776.........70145916........30189380016.....13004327687556

%C .....3936......10937316......30189380016.....83436203795656.230598746057340176

%C ....41216.....734979136...13004327687556.230598746057340176

%C ...431616...49393306556.5601924832399656

%C ..4519936.3319433387656

%C .47333376

%H R. H. Hardin, <a href="/A198642/b198642.txt">Table of n, a(n) for n = 1..39</a>

%e Some solutions for n=2 k=2

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Oct 27 2011