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Number of (n+2)X(1+2) 0..3 arrays with every consecutive three elements in every row and column having exactly two distinct values, and new values 0 upwards introduced in row major order
1

%I #5 Dec 24 2014 15:34:38

%S 384,2793,19320,139968,997740,7214139,51847038,374336607,2696923686,

%T 19459081686,140297901972,1012028831673,7298315687514,52640843328243,

%U 379651206972726,2738231536548126,19748883398358408,142436977913933235

%N Number of (n+2)X(1+2) 0..3 arrays with every consecutive three elements in every row and column having exactly two distinct values, and new values 0 upwards introduced in row major order

%C Column 1 of A252904

%H R. H. Hardin, <a href="/A252899/b252899.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 11*a(n-1) -7*a(n-2) -209*a(n-3) +345*a(n-4) +556*a(n-5) +2595*a(n-6) -5153*a(n-7) -22977*a(n-8) +2730*a(n-9) +70674*a(n-10) +123435*a(n-11) -145260*a(n-12) -314385*a(n-13) +142857*a(n-14) +214776*a(n-15) -26298*a(n-16) -31806*a(n-17) +2187*a(n-18)

%e Some solutions for n=4

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

%e ..0..2..2....1..2..1....2..3..3....2..2..1....1..1..0....1..2..1....1..2..2

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

%e ..1..1..3....1..0..0....2..1..1....2..1..1....0..0..2....0..3..0....0..0..2

%e ..0..0..3....1..2..2....2..3..3....0..2..0....3..1..1....3..2..2....1..0..1

%e ..0..1..0....2..2..0....1..1..3....0..1..1....3..1..1....3..3..0....1..1..2

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 24 2014