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A198179 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

%I A198179 #10 May 14 2018 08:46:54
%S A198179 0,4,3,8,16,21,56,70,171,256,516,905,1622,3048,5293,9992,17564,32517,
%T A198179 58330,106144,192767,348188,634426,1145535,2084360,3771658,6847617,
%U A198179 12413706,22507930,40835531,74015802,134288434,243440863,441575714
%N A198179 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.
%C A198179 Every 0 is next to 0 0'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 0's.
%C A198179 Column 2 of A198185.
%H A198179 R. H. Hardin, <a href="/A198179/b198179.txt">Table of n, a(n) for n = 1..200</a>
%F A198179 Empirical: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) -2*a(n-5) +4*a(n-7) -a(n-8) -3*a(n-9).
%F A198179 Empirical g.f.: x^2*(4 + 3*x - 4*x^2 - x^3 - x^4 + 6*x^5 - 3*x^6 - 7*x^7) / ((1 - x)*(1 + x - 2*x^2 - 4*x^3 - 2*x^4 - 4*x^7 - 3*x^8)). - _Colin Barker_, May 14 2018
%e A198179 All solutions for n=4:
%e A198179 ..1..2....2..1....1..0....0..1....1..2....1..0....0..1....2..1
%e A198179 ..0..1....1..0....2..1....1..2....0..1....2..1....1..2....1..0
%e A198179 ..2..1....0..1....0..1....1..0....1..0....2..1....1..2....1..2
%e A198179 ..1..0....1..2....1..2....2..1....2..1....1..0....0..1....0..1
%Y A198179 Cf. A198185.
%K A198179 nonn
%O A198179 1,2
%A A198179 _R. H. Hardin_, Oct 21 2011