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%I #7 Dec 11 2015 21:25:36
%S 306,972,3168,11205,35922,123357,408198,1376754,4572942,15438600,
%T 51367338,172747923,576448980,1935886518,6465571452,21695411226,
%U 72514916274,243164479179,813186470136,2725748659476,9118451550024
%N Number of (n+1) X 3 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 2 of A206277.
%H R. H. Hardin, <a href="/A206271/b206271.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-2) +28*a(n-4) +36*a(n-5) -18*a(n-6) +78*a(n-7) -490*a(n-8) +298*a(n-9) +86*a(n-10) -854*a(n-11) +1669*a(n-12) -524*a(n-13) -872*a(n-14) +648*a(n-15) +140*a(n-16) -302*a(n-17) +10*a(n-18) +76*a(n-19) +8*a(n-20) -16*a(n-21) +8*a(n-22) for n>24.
%e Some solutions for n=4:
%e ..2..0..2....1..2..0....0..1..1....0..2..2....2..1..0....0..0..0....1..2..1
%e ..1..1..0....1..0..1....2..1..1....0..1..2....2..2..1....1..2..0....0..1..1
%e ..1..1..0....2..1..1....0..2..2....0..0..1....2..2..2....1..2..1....0..0..2
%e ..1..2..1....2..1..1....0..2..2....0..0..1....0..2..2....0..0..2....2..1..0
%e ..0..1..1....0..2..1....1..0..2....2..1..2....2..0..2....0..0..1....1..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 05 2012