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Number of (n+1)X3 0..2 arrays with every 2X2 subblock having nonzero determinant and having the same number of clockwise edge increases as its horizontal and vertical neighbors
1

%I #5 Mar 31 2012 12:37:10

%S 170,798,3692,18572,93582,491162,2591052,13911368,74969572,406919686,

%T 2213161518,12071381806,65906319904,360238467670,1969917835712,

%U 10777127170178,58971800185530,322748974999228,1766538020755034

%N Number of (n+1)X3 0..2 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 A206128

%H R. H. Hardin, <a href="/A206122/b206122.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +24*a(n-2) -109*a(n-3) -170*a(n-4) +664*a(n-5) +290*a(n-6) -954*a(n-7) -69*a(n-8) +1074*a(n-9) -119*a(n-10) -639*a(n-11) +479*a(n-12) +61*a(n-13) -299*a(n-14) +97*a(n-15) +36*a(n-16) -24*a(n-17) +4*a(n-18) for n>19

%e Some solutions for n=4

%e ..2..1..0....1..2..0....2..2..1....0..2..0....0..1..2....2..0..1....2..1..1

%e ..2..2..2....1..0..1....2..1..1....1..2..2....1..0..1....2..1..2....2..2..1

%e ..2..1..2....0..1..2....1..1..2....1..1..2....2..1..0....0..2..1....1..2..2

%e ..0..1..1....2..2..0....1..2..2....0..1..1....1..0..2....1..0..2....2..2..1

%e ..1..1..0....1..0..1....1..1..2....1..1..0....2..1..0....2..1..0....2..0..1

%K nonn

%O 1,1

%A _R. H. Hardin_ Feb 04 2012