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A240888 Number of n X 3 0..2 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

%I A240888 #7 Oct 29 2018 06:43:16
%S A240888 2,11,57,289,1485,7609,38981,199761,1023597,5245049,26876501,
%T A240888 137719297,705694973,3616090505,18529407461,94947553233,486525966349,
%U A240888 2493034391385,12774694280053,65459511713057,335424674724381,1718767975363881
%N A240888 Number of n X 3 0..2 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.
%H A240888 R. H. Hardin, <a href="/A240888/b240888.txt">Table of n, a(n) for n = 1..210</a>
%F A240888 Empirical: a(n) = 3*a(n-1) + 8*a(n-2) + 14*a(n-3) + 4*a(n-4).
%F A240888 Empirical g.f.: x*(2 + 5*x + 8*x^2 + 2*x^3) / (1 - 3*x - 8*x^2 - 14*x^3 - 4*x^4). - _Colin Barker_, Oct 29 2018
%e A240888 Some solutions for n=4:
%e A240888 ..0..1..0....0..1..2....0..1..1....0..1..0....0..1..2....0..1..1....0..1..0
%e A240888 ..2..0..1....2..0..0....2..1..1....2..0..2....1..0..1....2..1..1....1..0..1
%e A240888 ..0..1..2....1..0..0....1..0..2....0..2..0....2..1..0....1..2..2....0..2..0
%e A240888 ..1..0..1....2..1..2....2..1..0....1..0..1....0..2..1....0..2..2....2..1..2
%Y A240888 Column 3 of A240893.
%K A240888 nonn
%O A240888 1,1
%A A240888 _R. H. Hardin_, Apr 14 2014