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%I #10 Feb 04 2014 09:55:57
%S 3,6,18,42,108,274,692,1754,4442,11248,28488,72146,182712,462728,
%T 1171876,2967826,7516146,19034954,48206826,122085820,309187486,
%U 783030352,1983057390,5022176478,12718873752,32211084212,81575929322,206594481604
%N Number of nX4 0..4 arrays with each element equal to the number its horizontal and vertical zero neighbors.
%C Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 0's, every 3 is next to 3 0's, every 4 is next to 4 0's.
%C Column 4 of A197054.
%H R. H. Hardin, <a href="/A197050/b197050.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) +3*a(n-2) +3*a(n-3) -a(n-4) -2*a(n-5) -a(n-6) for n>7.
%F Equivalent empirical G.f. 3*x -2*x^2*(1+x)*(x^4+3*x^3-3*x-3) ) / ( 1-x-3*x^2-3*x^3+x^4+2*x^5+x^6 ) . - R. J. Mathar, Oct 10 2011
%e Some solutions for n=5
%e ..0..2..1..0....2..0..3..0....0..3..0..2....2..0..3..0....0..3..0..1
%e ..3..0..2..1....0..4..0..3....3..0..4..0....0..4..0..3....2..0..2..1
%e ..0..4..0..2....2..0..4..0....0..4..0..2....3..0..3..0....1..1..2..0
%e ..3..0..4..0....1..2..0..3....3..0..2..1....0..2..1..1....0..3..0..3
%e ..0..3..0..2....0..1..2..0....0..2..1..0....1..1..0..1....2..0..3..0
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 09 2011
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