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%I #7 Dec 13 2015 18:46:00
%S 423,2691,17844,119727,815847,5593611,38594841,267189276,1854776850,
%T 12896494731,89778289281,625461045417,4359732229497,30399727224177,
%U 212022747357321,1478983212563424,10317870774963420,71985922839937911
%N Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases in its adjacent leftward and upward neighbors.
%C Column 2 of A206668.
%H R. H. Hardin, <a href="/A206662/b206662.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 14*a(n-1) -37*a(n-2) -242*a(n-3) +1172*a(n-4) +717*a(n-5) -9633*a(n-6) +5674*a(n-7) +31176*a(n-8) -35091*a(n-9) -39354*a(n-10) +60926*a(n-11) +15852*a(n-12) -33558*a(n-13) -12834*a(n-14) +15013*a(n-15) +2888*a(n-16) -2402*a(n-17) -318*a(n-18) -11*a(n-19) +49*a(n-20) for n>22.
%e Some solutions for n=4:
%e ..2..2..0....2..1..1....0..1..0....2..1..0....1..2..0....2..2..0....2..0..1
%e ..0..2..2....1..1..2....1..2..1....2..1..2....0..2..0....1..2..0....2..0..1
%e ..0..2..0....0..1..2....2..1..0....2..0..1....0..2..2....2..2..0....0..0..0
%e ..2..2..2....1..1..1....0..2..1....1..2..0....2..2..1....2..0..0....1..1..2
%e ..2..0..0....0..1..0....1..0..2....0..1..0....0..2..2....2..2..2....2..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 11 2012
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