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

%I #9 Mar 01 2018 14:31:16

%S 1,5,16,47,154,496,1601,5183,16777,54298,175777,569008,1841952,

%T 5962675,19302067,62483633,202268864,654774451,2119602518,6861469468,

%U 22211599969,71902261547,232758343993,753473472226,2439106000077,7895749882524

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

%C Column 2 of A197207.

%H R. H. Hardin, <a href="/A197201/b197201.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) + 4*a(n-2) + 2*a(n-3) - 4*a(n-4) - 8*a(n-5) + a(n-7) + 2*a(n-8).

%F Empirical g.f.: x*(1 + x)*(1 + 2*x - 7*x^3 - 3*x^4 - x^5 + 4*x^6) / (1 - 2*x - 4*x^2 - 2*x^3 + 4*x^4 + 8*x^5 - x^7 - 2*x^8). - _Colin Barker_, Mar 01 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A197207.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 11 2011