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%I #5 Mar 31 2012 12:37:07
%S 1262,17674,274013,4570761,77757894,1336717872,23044169753,
%T 397824057617,6870394713491,118674185578745,2049983501229713,
%U 35412502271123185,611737278096686056,10567570355635198190,182551538976364797431
%N Number of (n+1)X3 0..3 arrays with every 2X2 subblock having nonzero determinant and having the same number of clockwise edge increases as its horizontal and vertical neighbors
%C Column 2 of A205768
%H R. H. Hardin, <a href="/A205762/b205762.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 12*a(n-1) +180*a(n-2) -1118*a(n-3) -9765*a(n-4) +31210*a(n-5) +253507*a(n-6) -319680*a(n-7) -3638672*a(n-8) +371647*a(n-9) +28462890*a(n-10) +18822973*a(n-11) -110576923*a(n-12) -155454508*a(n-13) +84875372*a(n-14) +485465842*a(n-15) +833781515*a(n-16) -1004026264*a(n-17) -1450365072*a(n-18) +1484932044*a(n-19) -2084501770*a(n-20) -4315753720*a(n-21) +18885838458*a(n-22) -23502613968*a(n-23) +18179226965*a(n-24) -622240448*a(n-25) -20225966219*a(n-26) +11152325981*a(n-27) +11273987342*a(n-28) -5884555653*a(n-29) -14747346492*a(n-30) +25233454259*a(n-31) -21559347453*a(n-32) +2947343031*a(n-33) +17880881633*a(n-34) -23930581832*a(n-35) +17085474206*a(n-36) -7895668132*a(n-37) +1538961825*a(n-38) +1720201218*a(n-39) -2823763166*a(n-40) +2665078292*a(n-41) -1957039863*a(n-42) +1149111858*a(n-43) -527290946*a(n-44) +185703202*a(n-45) -48356745*a(n-46) +7996984*a(n-47) +44423*a(n-48) -604690*a(n-49) +259181*a(n-50) -74142*a(n-51) +15043*a(n-52) -1930*a(n-53) +149*a(n-54) -6*a(n-55)
%e Some solutions for 5X5
%e ..1..0..1....3..2..3....0..1..3....0..1..0....1..1..2....3..0..1....3..0..3
%e ..0..1..2....1..0..1....2..3..1....1..1..3....2..1..1....3..2..1....2..2..0
%e ..1..2..1....2..1..2....1..1..3....0..1..1....0..1..0....1..3..2....1..3..1
%e ..3..3..2....3..2..0....3..2..1....1..1..2....1..1..1....1..0..3....2..0..2
%e ..1..0..3....0..3..1....0..3..2....3..1..1....3..0..1....0..3..0....2..1..3
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 30 2012
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