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%I #12 Jun 15 2018 11:01:47
%S 81,306,1233,4884,19509,77580,309057,1230480,4900461,19512618,
%T 77701857,309412494,1232105853,4906303206,19537226541,77798456808,
%U 309798343185,1233636035952,4912416015885,19561547012604,77895299289393
%N Number of (n+1) X 2 0..2 arrays with no 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases in its adjacent leftward or upward neighbors.
%C Column 1 of A206277.
%H R. H. Hardin, <a href="/A206270/b206270.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-2) + 20*a(n-3) + 58*a(n-4) + 66*a(n-5) + 29*a(n-6) + 16*a(n-7).
%F Empirical g.f.: 3*x*(27 + 102*x + 249*x^2 + 476*x^3 + 431*x^4 + 174*x^5 + 88*x^6) / (1 - 6*x^2 - 20*x^3 - 58*x^4 - 66*x^5 - 29*x^6 - 16*x^7). - _Colin Barker_, Jun 15 2018
%e Some solutions for n=4:
%e ..1..0....2..1....0..1....1..1....2..1....2..0....1..1....2..2....2..1....1..1
%e ..0..2....2..0....2..0....1..0....1..1....1..2....0..1....1..2....0..2....1..2
%e ..1..1....2..0....2..2....2..1....1..1....1..2....2..1....0..2....1..2....1..0
%e ..2..0....2..1....1..0....2..2....0..1....1..0....0..2....2..0....2..2....2..1
%e ..0..0....0..2....2..1....2..2....2..2....2..1....2..2....0..0....1..0....1..1
%Y Cf. A206277.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 05 2012
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