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%I #7 Dec 11 2015 21:29:47
%S 1976,19688,205804,2410188,30417316,406202048,5614757320,79279051900,
%T 1133551023068,16329866489724,236305160608480,3428820549535568,
%U 49835495378403580,725069135358564372,10555976174903018132
%N Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having the same number of clockwise edge increases as its horizontal neighbors and the same number of counterclockwise edge increases as its vertical neighbors.
%C Column 2 of A206188.
%H R. H. Hardin, <a href="/A206182/b206182.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 39*a(n-1) -556*a(n-2) +3335*a(n-3) -3440*a(n-4) -55227*a(n-5) +256962*a(n-6) -264811*a(n-7) -857868*a(n-8) +2548311*a(n-9) -2287027*a(n-10) +1800223*a(n-11) -3079047*a(n-12) -3239297*a(n-13) +15341083*a(n-14) -33571111*a(n-15) +124436023*a(n-16) -246731438*a(n-17) +105761496*a(n-18) +314304308*a(n-19) -483127441*a(n-20) +175692193*a(n-21) +179821750*a(n-22) -267390162*a(n-23) +181386966*a(n-24) -79145409*a(n-25) +21749346*a(n-26) -4085634*a(n-27) +885924*a(n-28) -156240*a(n-29) +6750*a(n-30) for n>31.
%e Some solutions for n=4:
%e ..3..1..1....0..3..0....2..2..1....2..2..0....1..2..3....2..2..1....1..0..1
%e ..3..3..1....1..3..3....0..3..2....2..3..0....2..3..1....2..1..1....0..1..2
%e ..1..1..1....2..1..0....0..3..1....0..0..1....1..2..3....1..1..3....1..2..1
%e ..3..3..1....3..1..0....3..3..0....2..1..3....3..0..1....0..1..3....2..3..2
%e ..0..3..1....3..0..0....1..0..1....2..1..2....0..3..0....2..1..0....0..1..3
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 04 2012
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