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Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,1,0,1 for x=0,1,2,3,4.
1

%I #9 Jun 10 2014 03:54:48

%S 2,16,102,596,3713,22742,139212,853186,5231300,32071177,196597389,

%T 1205159672,7387795113,45288409942,277625447176,1701887549750,

%U 10432835696321,63954921521562,392053737458675,2403351095713061

%N Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,1,0,1 for x=0,1,2,3,4.

%C Every 0 is next to 0 4's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 1's.

%C Column 3 of A197805.

%H R. H. Hardin, <a href="/A197800/b197800.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) +6*a(n-2) +55*a(n-3) +93*a(n-4) +335*a(n-5) +452*a(n-6) +139*a(n-7) -1793*a(n-8) -3659*a(n-9) -6365*a(n-10) -7501*a(n-11) -3080*a(n-12) +14194*a(n-13) +48711*a(n-14) +46798*a(n-15) +16724*a(n-16) -51146*a(n-17) -68258*a(n-18) -58699*a(n-19) -12222*a(n-20) +5431*a(n-21) +7158*a(n-22) +52233*a(n-23) +9954*a(n-24) +5396*a(n-25) +905*a(n-26) -3014*a(n-27) +1824*a(n-28) +1787*a(n-29) -198*a(n-30) -430*a(n-31) -72*a(n-32).

%e Some solutions for n=4:

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 18 2011