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%I #7 Dec 13 2015 01:25:21
%S 81,423,423,2457,5199,2457,15087,69585,69585,15087,94761,953865,
%T 2073999,953865,94761,600519,13148043,62351943,62351943,13148043,
%U 600519,3818649,181467207,1876995285,4099250889,1876995285,181467207,3818649,24314127
%N T(n,k) = number of (n+1) X (k+1) 0..2 arrays with every 2 X 3 or 3 X 2 subblock having an equal number of clockwise and counterclockwise edge increases.
%C Table starts
%C .......81.........423...........2457.............15087.................94761
%C ......423........5199..........69585............953865..............13148043
%C .....2457.......69585........2073999..........62351943............1876995285
%C ....15087......953865.......62351943........4099250889..........269845754715
%C ....94761....13148043.....1876995285......269845754715........38883964087761
%C ...600519...181467207....56515649709....17769571483479......5607670598448153
%C ..3818649..2505335985..1701726564411..1170258128101905....808953988411331487
%C .24314127.34591087977.51240524315871.77072446958972853.116711118064834566675
%H R. H. Hardin, <a href="/A206414/b206414.txt">Table of n, a(n) for n = 1..143</a>
%e Some solutions for n=4, k=3:
%e ..1..2..0..2....0..1..2..0....2..1..1..1....0..1..2..0....0..1..1..1
%e ..1..1..2..2....1..0..1..2....2..1..1..2....1..2..2..0....0..2..0..2
%e ..1..2..2..1....1..1..2..0....1..1..1..1....0..1..1..2....0..1..0..1
%e ..2..0..2..2....0..1..2..2....1..2..2..1....0..1..2..1....2..1..2..1
%e ..2..0..0..2....2..0..1..1....2..2..1..0....2..0..1..0....2..0..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 07 2012
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