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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 2,0,1,3,4 for x=0,1,2,3,4.
1

%I #9 May 08 2018 06:20:01

%S 3,9,14,23,43,78,139,249,450,815,1475,2674,4859,8841,16102,29359,

%T 53587,97894,178971,327425,599394,1097871,2011875,3688402,6764595,

%U 12410585,22775742,41808791,76765147,140977582,258949451,475718009,874068802

%N 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 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 Column 2 of A195978.

%H R. H. Hardin, <a href="/A195972/b195972.txt">Table of n, a(n) for n = 1..200</a>

%F 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 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 Some solutions for n=4:

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

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

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

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

%Y Cf. A195978.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 25 2011