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A197883 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

%I A197883 #9 May 14 2018 06:34:30
%S A197883 0,4,3,14,18,43,78,154,305,572,1178,2185,4440,8408,16795,32212,63608,
%T A197883 123295,241494,470486,918795,1793434,3497978,6831997,13324168,
%U A197883 26019470,50755921,99095168,193344576,377408195,736481712,1437442548,2805273219
%N A197883 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.
%C A197883 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 1's, every 4 is next to 4 1's.
%C A197883 Column 2 of A197889.
%H A197883 R. H. Hardin, <a href="/A197883/b197883.txt">Table of n, a(n) for n = 1..200</a>
%F A197883 Empirical: a(n) = 3*a(n-2) +2*a(n-3) +a(n-4) -3*a(n-5) -4*a(n-6) +7*a(n-7) -5*a(n-9).
%F A197883 Empirical g.f.: x^2*(4 + 3*x + 2*x^2 + x^3 - 9*x^4 + 5*x^5 - 7*x^7) / ((1 - x)*(1 + x - 2*x^2 - 4*x^3 - 5*x^4 - 2*x^5 + 2*x^6 - 5*x^7 - 5*x^8)). - _Colin Barker_, May 14 2018
%e A197883 Some solutions for n=4:
%e A197883 ..2..1....2..1....1..2....1..2....2..1....1..2....0..1....2..1....0..1....1..2
%e A197883 ..1..3....1..3....3..1....3..1....1..0....0..1....1..2....1..0....1..2....0..1
%e A197883 ..3..1....0..1....1..3....1..0....1..2....2..1....1..2....3..1....1..0....1..0
%e A197883 ..1..2....1..2....2..1....2..1....0..1....1..0....0..1....1..2....2..1....2..1
%Y A197883 Cf. A197889.
%K A197883 nonn
%O A197883 1,2
%A A197883 _R. H. Hardin_, Oct 19 2011