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Number of nX2 0..3 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..3 introduced in row major order
1

%I #5 Apr 12 2014 15:44:27

%S 1,5,28,196,1418,10314,75138,547557,3990640,29085026,211983034,

%T 1545021626,11260787296,82073558277,598188294684,4359860795616,

%U 31776595508282,231601902583978,1688017273760974,12303017833728109

%N Number of nX2 0..3 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..3 introduced in row major order

%C Column 2 of A240774

%H R. H. Hardin, <a href="/A240770/b240770.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) -36*a(n-2) +4*a(n-3) +51*a(n-4) +74*a(n-5) -105*a(n-6) -60*a(n-7) +22*a(n-8) +66*a(n-9) -27*a(n-10) for n>11

%e Some solutions for n=4

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 12 2014