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%I #8 May 22 2018 05:42:07
%S 2,8,18,47,118,273,585,1174,2228,4030,6992,11697,18950,29839,45807,
%T 68736,101044,145796,206830,288899,397830,540701,726037,964026,
%U 1266756,1648474,2125868,2718373,3448502,4342203,5429243,6743620,8324004,10214208
%N Number of n X 3 0..1 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.
%C Column 3 of A201353.
%H R. H. Hardin, <a href="/A201348/b201348.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/5040)*n^7 - (1/720)*n^6 + (37/720)*n^5 - (53/144)*n^4 + (239/90)*n^3 - (2927/360)*n^2 + (1931/140)*n - 4 for n>1.
%F Conjectures from _Colin Barker_, May 22 2018: (Start)
%F G.f.: x*(2 - 8*x + 10*x^2 + 15*x^3 - 62*x^4 + 85*x^5 - 59*x^6 + 20*x^7 - 2*x^8) / (1 - x)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>9.
%F (End)
%e Some solutions for n=10:
%e ..0..0..1....0..0..0....0..0..1....0..0..1....0..0..0....0..0..1....0..0..1
%e ..0..0..1....0..1..1....0..1..1....0..0..1....0..1..1....0..0..1....0..0..1
%e ..0..1..0....1..0..0....0..1..1....0..0..1....0..1..1....0..1..0....0..1..0
%e ..0..1..0....1..0..0....1..1..0....0..0..1....0..1..1....0..1..0....0..1..0
%e ..0..1..1....1..0..0....1..1..0....0..1..0....0..1..1....0..1..1....0..1..1
%e ..0..1..1....1..0..0....1..1..1....0..1..0....0..1..1....1..0..1....0..1..1
%e ..1..0..1....1..0..1....1..1..1....0..1..0....0..1..1....1..0..1....0..1..1
%e ..1..0..1....1..0..1....1..1..1....0..1..1....0..1..1....1..0..1....0..1..1
%e ..1..0..1....1..0..1....1..1..1....1..0..0....1..0..0....1..1..0....1..0..0
%e ..1..1..1....1..1..1....1..1..1....1..1..0....1..0..0....1..1..0....1..0..0
%Y Cf. A201353.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 30 2011
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