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A208087 Number of 6 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.

%I A208087 #8 Jun 27 2018 14:17:54
%S A208087 72,168,402,1032,2664,6954,18168,47544,124434,325752,852792,2232618,
%T A208087 5845032,15302472,40062354,104884584,274591368,718889514,1882077144,
%U A208087 4927341912,12899948562,33772503768,88417562712,231480184362
%N A208087 Number of 6 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.
%C A208087 Row 5 of A208085.
%H A208087 R. H. Hardin, <a href="/A208087/b208087.txt">Table of n, a(n) for n = 1..210</a>
%F A208087 Empirical: a(n) = 3*a(n-1) - 3*a(n-3) + a(n-4).
%F A208087 Conjectures from _Colin Barker_, Jun 27 2018: (Start)
%F A208087 G.f.: 6*x*(12 - 8*x - 17*x^2 + 7*x^3) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)).
%F A208087 a(n) = (3/5)*2^(1-n)*(2^n*(15+2*(-1)^n) + (9-4*sqrt(5))*(3-sqrt(5))^n + (3+sqrt(5))^n*(9+4*sqrt(5))).
%F A208087 (End)
%e A208087 Some solutions for n=4:
%e A208087 ..0..1..0..1..1....0..0..0..0..1....0..0..1..0..1....0..0..0..1..0
%e A208087 ..0..1..0..1..0....1..1..1..1..1....1..0..1..0..1....1..1..1..1..1
%e A208087 ..1..0..1..0..1....1..1..1..1..1....0..1..0..1..0....1..1..1..1..1
%e A208087 ..1..0..1..0..1....0..1..0..1..0....0..0..0..0..0....1..0..1..0..1
%e A208087 ..0..1..0..1..0....1..0..1..0..1....0..0..0..0..0....0..1..0..1..0
%e A208087 ..0..0..0..0..0....0..0..1..1..1....1..0..1..0..1....1..1..0..1..0
%Y A208087 Cf. A208085.
%K A208087 nonn
%O A208087 1,1
%A A208087 _R. H. Hardin_, Feb 23 2012