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%I #9 May 11 2018 09:55:48
%S 1,3,10,25,81,242,707,2095,6224,18499,54863,162682,482707,1432377,
%T 4249808,12608401,37408069,110988820,329298679,977007545,2898720410,
%U 8600339717,25516721819,75706627806,224617138645,666426019913
%N Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,3,4,1,0 for x=0,1,2,3,4.
%C Every 0 is next to 0 2's, every 1 is next to 1 3's, every 2 is next to 2 4's, every 3 is next to 3 1's, every 4 is next to 4 0's.
%C Column 3 of A196989.
%H R. H. Hardin, <a href="/A196984/b196984.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = a(n-1) +2*a(n-2) +6*a(n-3) +11*a(n-4) +14*a(n-5) +4*a(n-6) -4*a(n-7) -4*a(n-8) -a(n-9).
%F Empirical g.f.: x*(1 + 2*x + 5*x^2 + 3*x^3 + 7*x^4 + 4*x^5 - 3*x^6 - 5*x^7 - 2*x^8) / (1 - x - 2*x^2 - 6*x^3 - 11*x^4 - 14*x^5 - 4*x^6 + 4*x^7 + 4*x^8 + x^9). - _Colin Barker_, May 11 2018
%e Some solutions for n=4:
%e ..0..0..0....0..0..1....1..3..1....1..0..0....0..0..1....0..1..0....0..0..0
%e ..0..1..0....0..1..3....0..1..1....3..1..1....1..1..3....1..3..1....0..0..1
%e ..1..3..1....0..1..1....0..1..3....1..1..3....3..1..1....0..0..0....0..1..3
%e ..0..0..0....1..3..1....0..0..1....0..0..1....1..0..0....0..0..0....0..0..1
%Y Cf. A196989.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 08 2011
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