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%I #5 Mar 31 2012 12:36:06
%S 0,704,704,2176,13440,2176,30976,253312,253312,30976,166272,4615296,
%T 7946432,4615296,166272,1567936,86388160,394724320,394724320,86388160,
%U 1567936,10419200,1613838400,15491352288,39825200832,15491352288
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock trace equal to exactly one or two horizontal and vertical neighbor 2X2 subblock traces
%C Table starts
%C ..........0............704.............2176.............30976
%C ........704..........13440...........253312...........4615296
%C .......2176.........253312..........7946432.........394724320
%C ......30976........4615296........394724320.......39825200832
%C .....166272.......86388160......15491352288.....3861027028096
%C ....1567936.....1613838400.....686342587904...380882328583712
%C ...10419200....30161413056...28533024476512.37393297725524928
%C ...85438016...563483938112.1225810619871552
%C ..615338112.10530498631296
%C .4793908736
%H R. H. Hardin, <a href="/A186923/b186923.txt">Table of n, a(n) for n = 1..60</a>
%e Some solutions for 4X3
%e ..0..1..0....2..2..0....2..2..1....2..0..1....2..2..0....0..2..2....0..1..3
%e ..3..2..1....1..3..3....0..3..3....2..1..3....3..1..1....2..3..1....2..2..1
%e ..1..2..3....3..3..2....2..3..2....3..0..1....0..0..2....3..2..1....3..1..2
%e ..3..2..1....0..1..2....2..1..0....3..0..3....0..0..0....1..0..1....1..0..3
%Y Column 1 is A185799
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Feb 28 2011