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Number of 2 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.
1

%I #8 Oct 30 2018 09:39:02

%S 2,7,28,121,523,2261,9775,42261,182711,789933,3415199,14765285,

%T 63836295,275990109,1193216815,5158758677,22303399319,96426611981,

%U 416891226559,1802389311557,7792457656743,33689944754365,145655251212111

%N Number of 2 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="/A241371/b241371.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 2*a(n-2) - 4*a(n-3) for n>5.

%F Empirical g.f.: x*(1 - x - x^2)*(2 - x - 2*x^2) / (1 - 5*x + 2*x^2 + 4*x^3). - _Colin Barker_, Oct 30 2018

%e Some solutions for n=4:

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

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

%Y Row 2 of A241370.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 20 2014