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%I #4 Mar 31 2012 12:36:12
%S 0,704,704,1936,15776,1936,34816,315520,315520,34816,172992,6781400,
%T 11342816,6781400,172992,2053216,146491208,716732884,716732884,
%U 146491208,2053216,12950528,3204417424,34292827560
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock sum equal to exactly one or two horizontal and vertical neighbor 2X2 subblock sums
%C Table starts
%C .......0.......704......1936.....34816......172992....2053216.12950528
%C .....704.....15776....315520...6781400...146491208.3204417424
%C ....1936....315520..11342816.716732884.34292827560
%C ...34816...6781400.716732884
%C ..172992.146491208
%C .2053216
%e Some solutions for 3X3
%e ..2..1..2....2..3..2....3..0..2....3..3..2....2..3..2....0..1..0....0..1..0
%e ..0..0..0....2..3..0....3..0..2....3..3..3....1..1..1....0..2..0....3..3..3
%e ..2..1..2....2..3..2....2..1..1....3..3..2....3..0..3....1..3..1....0..2..0
%Y Column 1 is A185568
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Mar 29 2011