%I #8 Oct 30 2018 10:34:27

%S 5,47,460,4617,46245,463567,4646421,46573979,466838093,4679401043,

%T 46904463629,470151838595,4712616517773,47237408834627,

%U 473489150832621,4746068456910627,47572717892835405,476850156780960707

%N Number of 3 X n 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

%H R. H. Hardin, <a href="/A241372/b241372.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) + 16*a(n-2) - 50*a(n-3) - 72*a(n-4) - 32*a(n-5) - 32*a(n-6) for n>8.

%F Empirical g.f.: x*(5 + 2*x - 43*x^2 - 25*x^3 + 42*x^4 + 34*x^5 + 32*x^6 + 16*x^7) / (1 - 9*x - 16*x^2 + 50*x^3 + 72*x^4 + 32*x^5 + 32*x^6). - _Colin Barker_, Oct 30 2018

%e Some solutions for n=4:

%e ..0..1..0..2....0..1..0..0....0..1..2..0....0..1..0..2....0..1..1..2

%e ..2..1..1..2....1..2..0..0....0..1..0..1....0..0..1..2....0..1..1..2

%e ..2..1..1..0....2..0..1..2....1..2..0..2....2..0..1..2....2..1..2..0

%Y Row 3 of A241370.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 20 2014