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Number of nX3 0..4 arrays with each element equal to the number its horizontal and vertical neighbors unequal to itself
1

%I #5 Mar 31 2012 12:36:25

%S 2,6,10,16,21,44,82,144,273,531,1032,1960,3805,7446,14505,28254,55311,

%T 108511,212645,417039,819145,1609692,3163058,6217976,12229218,

%U 24055201,47320658,93104592,183213156,360551489,709578685,1396577604,2748853048

%N Number of nX3 0..4 arrays with each element equal to the number its horizontal and vertical neighbors unequal to itself

%C Column 3 of A195962

%H R. H. Hardin, <a href="/A195957/b195957.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-2) +5*a(n-3) +5*a(n-4) -4*a(n-5) -15*a(n-6) -14*a(n-7) -a(n-8) +10*a(n-9) +2*a(n-10) -16*a(n-11) -15*a(n-12) +9*a(n-13) +29*a(n-14) +20*a(n-15) -2*a(n-16) -10*a(n-17) -4*a(n-18)

%e Some solutions for n=5

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

%e ..2..2..2....2..3..2....3..4..3....3..4..3....3..4..3....1..1..1....1..1..3

%e ..3..4..3....2..3..2....2..2..2....2..2..2....2..2..2....1..1..1....1..1..1

%e ..2..2..2....3..4..3....3..4..3....3..4..3....3..4..3....3..4..3....3..4..1

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Sep 25 2011