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%I #12 Mar 27 2020 19:12:22
%S 2,4,8,14,23,36,54,78,109,148,196,254,323,404,498,606,729,868,1024,
%T 1198,1391,1604,1838,2094,2373,2676,3004,3358,3739,4148,4586,5054,
%U 5553,6084,6648,7246,7879,8548,9254,9998,10781,11604,12468,13374,14323,15316,16354
%N Number of n X 2 0..1 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.
%C Column 2 of A201353.
%H R. H. Hardin, <a href="/A201347/b201347.txt">Table of n, a(n) for n = 1..210</a>
%H Ângela Mestre, José Agapito, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Mestre/mestre2.html">Square Matrices Generated by Sequences of Riordan Arrays</a>, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.
%F Empirical: a(n) = (1/6)*n^3 - (1/2)*n^2 + (10/3)*n - 2 for n>1.
%F Conjectures from _Colin Barker_, May 22 2018: (Start)
%F G.f.: x*(2 - 4*x + 4*x^2 - 2*x^3 + x^4) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
%F (End)
%e Some solutions for n=10:
%e ..0..0....0..0....0..0....0..0....0..1....0..1....0..0....0..0....0..0....0..0
%e ..0..0....0..0....0..0....0..0....0..1....0..1....0..0....0..1....0..1....0..0
%e ..0..1....0..0....0..0....0..0....1..0....0..1....0..0....0..1....0..1....0..0
%e ..0..1....0..0....1..1....0..1....1..0....0..1....0..0....0..1....0..1....0..0
%e ..0..1....0..0....1..1....0..1....1..0....0..1....0..0....1..0....1..0....0..0
%e ..0..1....0..0....1..1....0..1....1..0....1..0....0..0....1..0....1..0....0..1
%e ..0..1....0..0....1..1....1..1....1..0....1..0....0..1....1..0....1..0....0..1
%e ..0..1....0..0....1..1....1..1....1..0....1..0....0..1....1..1....1..0....0..1
%e ..1..0....0..1....1..1....1..1....1..1....1..0....0..1....1..1....1..0....1..0
%e ..1..0....1..1....1..1....1..1....1..1....1..0....1..1....1..1....1..1....1..0
%t Rest@ CoefficientList[Series[x (2 - 4 x + 4 x^2 - 2 x^3 + x^4)/(1 - x)^4, {x, 0, 47}], x] (* _Michael De Vlieger_, Mar 27 2020 *)
%Y Cf. A201353.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 30 2011
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