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A196132 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,3,4 for x=0,1,2,3,4.

%I A196132 #8 May 08 2018 09:24:01
%S A196132 0,4,3,8,14,19,46,56,133,184,372,599,1064,1874,3147,5692,9516,17053,
%T A196132 28980,51004,88089,153086,266660,461205,804810,1392380,2426083,
%U A196132 4205680,7313450,12699273,22056242,38328650,66544359,115648570,200804584
%N A196132 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,3,4 for x=0,1,2,3,4.
%C A196132 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 3's, every 4 is next to 4 4's.
%C A196132 Column 2 of A196138.
%H A196132 R. H. Hardin, <a href="/A196132/b196132.txt">Table of n, a(n) for n = 1..200</a>
%F A196132 Empirical: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) -3*a(n-5) -a(n-6) +4*a(n-7) -2*a(n-9).
%F A196132 Empirical g.f.: x^2*(4 + 3*x - 4*x^2 - 3*x^3 - 3*x^4 + 6*x^5 - 4*x^7) / ((1 - x)*(1 + x - 2*x^2 - 4*x^3 - 2*x^4 + x^5 + 2*x^6 - 2*x^7 - 2*x^8)). - _Colin Barker_, May 08 2018
%e A196132 All solutions for n=4:
%e A196132 ..0..1....2..1....1..2....2..1....1..0....0..1....1..0....1..2
%e A196132 ..1..2....1..0....0..1....1..0....2..1....1..2....2..1....0..1
%e A196132 ..1..0....0..1....2..1....1..2....0..1....1..2....2..1....1..0
%e A196132 ..2..1....1..2....1..0....0..1....1..2....0..1....1..0....2..1
%Y A196132 Cf. A196138.
%K A196132 nonn
%O A196132 1,2
%A A196132 _R. H. Hardin_, Sep 28 2011