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%I #7 Oct 03 2018 14:08:54
%S 9,37,163,723,3209,14245,63235,280707,1246089,5531525,24555043,
%T 109002515,483874057,2147969733,9535072003,42327224963,187895169801,
%U 834087159397,3702603905187,16436262714579,72962363498889,323887892265317
%N Number of (n+1) X (1+1) 0..2 arrays with every element both >= and <= some horizontal or antidiagonal neighbor.
%H R. H. Hardin, <a href="/A232250/b232250.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) + 2*a(n-2) - a(n-4).
%F Empirical g.f.: x*(9 + x - 3*x^2 - 3*x^3) / (1 - 4*x - 2*x^2 + x^4). - _Colin Barker_, Oct 03 2018
%e Some solutions for n=6:
%e ..1..1....0..0....2..2....1..1....1..1....1..1....2..2....2..2....1..1....0..0
%e ..0..0....1..1....1..1....1..1....0..0....2..2....0..0....1..1....2..2....0..1
%e ..2..2....2..2....2..2....0..0....0..0....1..1....0..2....1..1....2..0....1..2
%e ..1..0....2..1....2..1....1..1....1..2....0..0....2..0....1..2....0..1....2..1
%e ..0..0....1..2....1..2....2..2....2..0....0..0....0..0....2..2....2..2....1..0
%e ..1..2....2..0....2..1....1..0....0..0....0..1....0..0....0..0....2..0....0..0
%e ..2..2....0..0....1..1....0..0....1..1....2..2....0..0....0..0....0..0....0..0
%Y Column 1 of A232257.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 21 2013
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