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%I #7 Oct 29 2018 05:59:23
%S 1,4,20,97,459,2187,10442,49861,238068,1136678,5427201,25912833,
%T 123723975,590735140,2820536641,13466994652,64299801122,307007207679,
%U 1465843189533,6998846289463,33416841401200,159552766705917
%N Number of n X 3 0..1 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..1 introduced in row major order.
%H R. H. Hardin, <a href="/A240778/b240778.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) - a(n-2) - a(n-3) + 4*a(n-4) - 4*a(n-5) - 3*a(n-6) + a(n-7).
%F Empirical g.f.: x*(1 + x)^2*(1 - 3*x + 6*x^2 - 7*x^3 + 2*x^4) / ((1 - x)*(1 - 4*x - 3*x^2 - 2*x^3 - 6*x^4 - 2*x^5 + x^6)). - _Colin Barker_, Oct 29 2018
%e Some solutions for n=4:
%e ..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0
%e ..0..1..1....1..0..1....0..1..0....0..1..0....0..1..0....1..0..1....1..1..0
%e ..0..1..1....0..1..1....1..0..1....1..1..0....0..0..1....1..1..0....1..0..0
%e ..0..1..0....0..1..0....0..1..0....1..1..0....1..0..1....0..1..0....1..0..0
%Y Column 3 of A240783.
%K nonn
%O 1,2
%A _R. H. Hardin_, Apr 12 2014
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