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A208556 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically.

%I A208556 #9 Mar 07 2018 06:23:26
%S A208556 9,81,225,1089,3969,16641,65025,263169,1046529,4198401,16769025,
%T A208556 67125249,268402689,1073807361,4294836225,17180131329,68718952449,
%U A208556 274878955521,1099509530625,4398050705409,17592177655809,70368760954881
%N A208556 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically.
%C A208556 Row 4 of A208555.
%C A208556 It seems that all terms are squares. - _Colin Barker_, Mar 07 2018
%H A208556 R. H. Hardin, <a href="/A208556/b208556.txt">Table of n, a(n) for n = 1..210</a>
%F A208556 Empirical: a(n) = 3*a(n-1) + 6*a(n-2) - 8*a(n-3).
%F A208556 Conjectures from _Colin Barker_, Mar 07 2018: (Start)
%F A208556 G.f.: 9*x*(1 + 6*x - 8*x^2) / ((1 - x)*(1 + 2*x)*(1 - 4*x)).
%F A208556 a(n) = (2^(n+1) + 1)^2 for n even.
%F A208556 a(n) = (2^(n+1) - 1)^2 for n odd.
%F A208556 (End)
%e A208556 Some solutions for n=4:
%e A208556 ..0..1..1..1....1..0..1..1....0..1..1..1....1..0..1..0....0..1..0..0
%e A208556 ..1..0..1..0....0..1..1..0....0..1..0..1....0..1..1..1....1..0..1..1
%e A208556 ..0..1..0..0....1..0..1..1....0..1..1..0....1..0..1..0....0..1..0..0
%e A208556 ..1..0..1..0....0..1..1..0....0..1..0..0....0..1..0..1....1..0..1..1
%Y A208556 Cf. A208555.
%K A208556 nonn
%O A208556 1,1
%A A208556 _R. H. Hardin_, Feb 28 2012