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%I #9 May 12 2018 08:45:58
%S 1,3,32,45,189,646,1873,6209,19883,62891,201940,644884,2058462,
%T 6580709,21022103,67159181,214583759,685563259,2190314160,6997940987,
%U 22357818950,71431546562,228218559544,729140737836,2329549699706,7442735684274
%N Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,4,1,0,1 for x=0,1,2,3,4.
%C Every 0 is next to 0 2's, every 1 is next to 1 4's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 1's.
%C Column 3 of A197373.
%H R. H. Hardin, <a href="/A197368/b197368.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) +2*a(n-2) +7*a(n-3) -3*a(n-4) -7*a(n-6) -5*a(n-7) +3*a(n-8).
%F Empirical g.f.: x*(1 + x + 24*x^2 - 32*x^3 + 17*x^4 - 37*x^5 - 9*x^6 + 9*x^7) / (1 - 2*x - 2*x^2 - 7*x^3 + 3*x^4 + 7*x^6 + 5*x^7 - 3*x^8). - _Colin Barker_, May 12 2018
%e Some solutions for n=4:
%e ..0..0..0....2..1..0....0..3..0....0..1..0....0..0..0....0..3..0....0..0..0
%e ..0..0..0....1..4..1....3..0..0....1..4..1....3..0..0....0..0..3....3..0..3
%e ..3..0..0....0..1..0....0..0..0....0..1..0....0..0..3....0..0..0....0..0..0
%e ..0..3..0....0..0..0....0..3..0....0..0..0....0..3..0....0..0..0....0..3..0
%Y Cf. A197373.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 14 2011
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