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A195972 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,3,4 for x=0,1,2,3,4.

%I A195972 #9 May 08 2018 06:20:01
%S A195972 3,9,14,23,43,78,139,249,450,815,1475,2674,4859,8841,16102,29359,
%T A195972 53587,97894,178971,327425,599394,1097871,2011875,3688402,6764595,
%U A195972 12410585,22775742,41808791,76765147,140977582,258949451,475718009,874068802
%N A195972 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,3,4 for x=0,1,2,3,4.
%C A195972 Every 0 is next to 0 2's, every 1 is next to 1 0'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 A195972 Column 2 of A195978.
%H A195972 R. H. Hardin, <a href="/A195972/b195972.txt">Table of n, a(n) for n = 1..200</a>
%F A195972 Empirical: a(n) = 2*a(n-1) +a(n-3) -a(n-4) -2*a(n-5) -2*a(n-6) -a(n-7).
%F A195972 Empirical g.f.: x*(1 + x)^2*(3 - 3*x - x^2 - 3*x^3 - 2*x^4) / ((1 + x^2)*(1 - x - x^2)*(1 - x - x^2 - x^3)). - _Colin Barker_, May 08 2018
%e A195972 Some solutions for n=4:
%e A195972 ..0..1....2..1....1..1....1..0....0..1....1..0....1..2....0..1....0..0....0..1
%e A195972 ..1..1....1..0....0..0....1..0....1..1....1..0....0..1....0..1....0..0....0..1
%e A195972 ..1..0....1..0....0..0....1..0....1..0....1..1....0..1....1..1....0..0....0..1
%e A195972 ..1..0....2..1....1..1....1..0....2..1....0..1....1..2....1..0....0..0....0..1
%Y A195972 Cf. A195978.
%K A195972 nonn
%O A195972 1,1
%A A195972 _R. H. Hardin_, Sep 25 2011