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A208086 Number of 4 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 A208086 #8 Jun 27 2018 14:17:42
%S A208086 24,56,134,344,888,2318,6056,15848,41478,108584,284264,744206,1948344,
%T A208086 5100824,13354118,34961528,91530456,239629838,627359048,1642447304,
%U A208086 4299982854,11257501256,29472520904,77160061454,202007663448
%N A208086 Number of 4 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 A208086 Row 3 of A208085.
%H A208086 R. H. Hardin, <a href="/A208086/b208086.txt">Table of n, a(n) for n = 1..210</a>
%F A208086 Empirical: a(n) = 3*a(n-1) - 3*a(n-3) + a(n-4).
%F A208086 Conjectures from _Colin Barker_, Jun 27 2018: (Start)
%F A208086 G.f.: 2*x*(12 - 8*x - 17*x^2 + 7*x^3) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)).
%F A208086 a(n) = 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))) / 5.
%F A208086 (End)
%e A208086 Some solutions for n=4:
%e A208086 ..0..0..1..0..0....0..0..0..1..1....0..0..0..1..0....0..1..0..1..0
%e A208086 ..1..1..1..1..1....0..1..0..1..0....0..1..0..1..0....1..0..1..0..1
%e A208086 ..1..1..1..1..1....1..0..1..0..1....1..0..1..0..1....1..0..1..0..1
%e A208086 ..0..1..0..1..0....1..1..1..1..1....1..0..0..0..0....0..1..0..1..0
%Y A208086 Cf. A208085.
%K A208086 nonn
%O A208086 1,1
%A A208086 _R. H. Hardin_, Feb 23 2012