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%I #10 Jun 11 2018 05:10:17
%S 20,52,132,340,868,2228,5700,14612,37412,95860,245508,628948,1610980,
%T 4126772,10570692,27077780,69360548,177671668,455113860,1165800532,
%U 2986255972,7649458100,19594481988,50192314388,128570242340,329339499892
%N Number of (n+1) X 3 0..1 arrays with the number of equal 2 X 2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..1 introduced in row major order.
%C Column 2 of A205226.
%D Equals A205219(n+1).
%H R. H. Hardin, <a href="/A205220/b205220.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) +4*a(n-2).
%F Conjectures from _Colin Barker_, Jun 11 2018: (Start)
%F G.f.: 4*x*(5 + 8*x) / (1 - x - 4*x^2).
%F a(n) = (2^(2-n)*((1-sqrt(17))^n*(-4+sqrt(17)) + (1+sqrt(17))^n*(4+sqrt(17)))) / sqrt(17).
%F (End)
%e Some solutions for n=4:
%e ..0..0..0....0..1..0....0..1..1....0..0..1....0..1..1....0..0..1....0..1..0
%e ..0..0..1....1..1..0....0..0..0....1..0..1....0..1..0....0..0..1....1..1..0
%e ..1..0..1....0..0..0....0..0..1....0..1..1....1..1..0....1..1..1....0..0..1
%e ..0..1..1....1..0..0....1..0..1....0..0..0....1..1..1....1..0..0....1..0..1
%e ..1..1..1....0..1..0....1..0..0....1..1..0....1..0..0....0..1..0....0..1..1
%Y Cf. A205226.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 23 2012
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