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%I #9 May 23 2018 08:11:29
%S 3,9,25,69,175,410,899,1859,3649,6840,12311,21378,35964,58819,93800,
%T 146222,223292,334639,492954,714755,1021293,1439616,2003809,2756429,
%U 3750155,5049674,6733825,8898024,11656994,15147825,19533390,25006144
%N Number of n X 2 0..2 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.
%C Column 2 of A201539.
%H R. H. Hardin, <a href="/A201533/b201533.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/40320)*n^8 - (1/3360)*n^7 + (23/2880)*n^6 - (1/48)*n^5 + (247/5760)*n^4 + (231/160)*n^3 - (6777/1120)*n^2 + (3121/168)*n - 20 for n>3.
%F Conjectures from _Colin Barker_, May 23 2018: (Start)
%F G.f.: x*(3 - 18*x + 52*x^2 - 84*x^3 + 76*x^4 - 25*x^5 - 19*x^6 + 20*x^7 + x^8 - 9*x^9 + 5*x^10 - x^11) / (1 - x)^9.
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>12.
%F (End)
%e Some solutions for n=10:
%e ..0..2....0..2....0..1....0..0....0..1....0..2....0..0....0..0....0..1....0..1
%e ..0..2....0..2....0..1....0..1....0..1....0..2....0..0....0..1....0..1....0..1
%e ..0..2....0..2....1..1....1..1....0..1....2..0....0..0....0..1....0..1....0..1
%e ..0..2....0..2....1..2....1..1....0..1....2..0....0..2....0..2....1..0....0..1
%e ..0..2....0..2....1..2....1..2....1..0....2..0....1..2....0..2....1..0....1..0
%e ..1..1....1..0....1..2....1..2....1..0....2..0....1..2....0..2....1..0....1..0
%e ..1..1....1..0....1..2....2..1....1..0....2..2....2..2....0..2....1..1....2..2
%e ..1..2....2..0....2..0....2..1....2..1....2..2....2..2....2..1....2..1....2..2
%e ..1..2....2..0....2..0....2..2....2..1....2..2....2..2....2..1....2..2....2..2
%e ..1..2....2..2....2..2....2..2....2..2....2..2....2..2....2..1....2..2....2..2
%Y Cf. A201539.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 02 2011
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