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Number of (n+1)X2 0..2 arrays containing all values 0..2 with every 2X2 subblock having two distinct values, and new values 0..2 introduced in row major order
1

%I #8 Mar 31 2012 12:37:31

%S 0,9,75,475,2695,14443,74831,379459,1896807,9388731,46152447,

%T 225762931,1100476759,5350600939,25966867823,125848830499,

%U 609324773703,2948038268955,14255607687903,68907738083539,332985156888631

%N Number of (n+1)X2 0..2 arrays containing all values 0..2 with every 2X2 subblock having two distinct values, and new values 0..2 introduced in row major order

%C Column 1 of A210052

%H R. H. Hardin, <a href="/A210045/b210045.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) -6*a(n-2) -20*a(n-3) -8*a(n-4).

%F Empirical G.f.: x^2*(3+2*x)^2/((1-3*x-2*x^2)*(1-4*x-4*x^2)). [Colin Barker, Mar 23 2012]

%e Some solutions for n=4

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Mar 16 2012