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Number of nX3 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero
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%I #4 Oct 31 2013 14:41:09

%S 0,2,14,34,198,810,3706,16918,76318,347442,1575090,7148582,32438126,

%T 147179442,667843250,3030291798,13749921166,62390019330,283093420626,

%U 1284531566502,5828537726158,26446883611922,120002248379506

%N Number of nX3 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero

%C Column 3 of A230899

%H R. H. Hardin, <a href="/A230894/b230894.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +3*a(n-2) -25*a(n-3) -8*a(n-4) +82*a(n-5) -8*a(n-6) -132*a(n-7) +80*a(n-8) +12*a(n-9) -32*a(n-10) +16*a(n-11)

%e Some solutions for n=4

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 31 2013