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%I #7 Dec 13 2015 21:21:31
%S 5352,55836,645144,7423464,84549024,965476188,11019153780,
%T 125824938768,1436467496004,16401282343620,187256077071780,
%U 2137984718567652,24409992616289508,278697654455164344,3181981888269341316
%N Number of (n+1) X 5 0..2 arrays with every 2 X 3 or 3 X 2 subblock having an unequal number of clockwise and counterclockwise edge increases.
%C Column 4 of A206685.
%H R. H. Hardin, <a href="/A206681/b206681.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) +71*a(n-2) +109*a(n-3) +304*a(n-4) +1749*a(n-5) +6190*a(n-6) +40798*a(n-7) +113760*a(n-8) +156451*a(n-9) +56935*a(n-10) -344927*a(n-11) -3135593*a(n-12) -2982120*a(n-13) -4186941*a(n-14) -4278189*a(n-15) +25395411*a(n-16) +21365207*a(n-17) +23528296*a(n-18) +18470333*a(n-19) +10691226*a(n-20) -158651917*a(n-21) +1474977*a(n-22) -90337878*a(n-23) +67235360*a(n-24) +78673890*a(n-25) +28641537*a(n-26) +12971893*a(n-27) -19013172*a(n-28) -10811757*a(n-29) +317677*a(n-30) +183847*a(n-31) -595959*a(n-32) +788026*a(n-33) +829709*a(n-34) +184148*a(n-35) +6927*a(n-36) -15576*a(n-37) -13017*a(n-38) -3018*a(n-39) -438*a(n-40) -72*a(n-41) for n>42.
%e Some solutions for n=4:
%e ..1..2..1..1..2....2..1..0..0..2....0..0..1..0..2....1..1..1..1..0
%e ..1..2..0..1..0....0..0..2..1..0....2..2..1..1..2....0..2..2..0..0
%e ..0..2..2..1..0....1..1..1..1..2....0..1..2..0..1....0..0..1..2..1
%e ..0..0..1..1..2....0..2..2..0..1....1..1..0..2..2....1..2..0..0..2
%e ..2..1..2..0..1....1..0..1..2..1....2..0..0..1..1....2..1..0..0..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 11 2012
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