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A208089 Number of 8 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 A208089 #11 Jun 28 2018 08:25:52
%S A208089 216,504,1206,3096,7992,20862,54504,142632,373302,977256,2558376,
%T A208089 6697854,17535096,45907416,120187062,314653752,823774104,2156668542,
%U A208089 5646231432,14782025736,38699845686,101317511304,265252688136,694440553086
%N A208089 Number of 8 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 A208089 Row 7 of A208085.
%H A208089 R. H. Hardin, <a href="/A208089/b208089.txt">Table of n, a(n) for n = 1..210</a>
%F A208089 Empirical: a(n) = 3*a(n-1) - 3*a(n-3) + a(n-4).
%F A208089 Conjectures from _Colin Barker_, Jun 28 2018: (Start)
%F A208089 G.f.: 18*x*(12 - 8*x - 17*x^2 + 7*x^3) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)).
%F A208089 a(n) = (9/5)*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 A208089 (End)
%e A208089 Some solutions for n=4:
%e A208089 ..0..1..0..0..1....0..0..0..1..0....0..1..0..0..1....0..0..0..1..1
%e A208089 ..1..1..1..1..1....0..1..0..1..0....1..1..1..1..1....0..1..0..1..0
%e A208089 ..1..1..1..1..1....1..0..1..0..1....1..1..1..1..1....1..0..1..0..1
%e A208089 ..1..0..1..0..1....1..0..1..0..1....0..1..0..1..0....0..0..0..0..0
%e A208089 ..0..1..0..1..0....0..1..0..1..0....1..0..1..0..1....0..0..0..0..0
%e A208089 ..1..1..1..1..1....0..1..0..1..0....0..0..0..0..0....1..1..1..1..1
%e A208089 ..1..1..1..1..1....1..0..1..0..1....0..0..0..0..0....1..1..1..1..1
%e A208089 ..1..0..1..0..1....0..0..0..0..0....1..0..1..1..0....0..0..1..0..0
%Y A208089 Cf. A208085.
%K A208089 nonn
%O A208089 1,1
%A A208089 _R. H. Hardin_, Feb 23 2012