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A208088 Number of 7 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 A208088 #8 Jun 27 2018 15:30:13
%S A208088 108,180,288,468,756,1224,1980,3204,5184,8388,13572,21960,35532,57492,
%T A208088 93024,150516,243540,394056,637596,1031652,1669248,2700900,4370148,
%U A208088 7071048,11441196,18512244,29953440,48465684,78419124,126884808
%N A208088 Number of 7 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 A208088 Row 6 of A208085.
%H A208088 R. H. Hardin, <a href="/A208088/b208088.txt">Table of n, a(n) for n = 1..210</a>
%F A208088 Empirical: a(n) = a(n-1) + a(n-2).
%F A208088 Conjectures from _Colin Barker_, Jun 27 2018: (Start)
%F A208088 G.f.: 36*x*(3 + 2*x) / (1 - x - x^2).
%F A208088 a(n) = (9*2^(2-n)*((1-sqrt(5))^n*(-2+sqrt(5)) + (1+sqrt(5))^n*(2+sqrt(5)))) / sqrt(5).
%F A208088 (End)
%e A208088 Some solutions for n=4:
%e A208088 ..0..0..0..1..0....0..1..0..1..1....0..0..0..0..0....0..0..0..1..0
%e A208088 ..0..1..0..1..0....0..0..0..0..0....0..1..0..1..0....1..1..1..1..1
%e A208088 ..1..0..1..0..1....0..0..0..0..0....1..0..1..0..1....1..1..1..1..1
%e A208088 ..1..0..1..0..1....1..0..1..0..1....0..0..0..0..0....1..0..1..0..1
%e A208088 ..0..1..0..1..0....0..1..0..1..0....0..0..0..0..0....0..1..0..1..0
%e A208088 ..1..1..1..1..1....0..0..0..0..0....0..1..0..1..0....0..1..0..1..0
%e A208088 ..1..1..1..1..1....0..0..0..0..0....1..0..1..0..1....1..0..1..0..1
%Y A208088 Cf. A208085.
%K A208088 nonn
%O A208088 1,1
%A A208088 _R. H. Hardin_, Feb 23 2012