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Number of (n+1) X 2 binary arrays with every 2 X 2 subblock trace equal to some horizontal or vertical neighbor 2 X 2 subblock trace.
2

%I #9 Feb 28 2018 06:51:51

%S 0,24,40,144,344,1000,2688,7528,20648,57040,156920,432648,1192128,

%T 3286216,9056584,24960464,68789400,189584296,522495232,1440006312,

%U 3968670312,10937688528,30144344504,83078054856,228963805504

%N Number of (n+1) X 2 binary arrays with every 2 X 2 subblock trace equal to some horizontal or vertical neighbor 2 X 2 subblock trace.

%C Column 1 of A185750.

%H R. H. Hardin, <a href="/A185742/b185742.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) + 8*a(n-4).

%F Empirical g.f.: 8*x^2*(3 - 4*x + 6*x^2) / (1 - 3*x + x^2 + 2*x^3 - 8*x^4). - _Colin Barker_, Feb 28 2018

%e Some solutions for 3 X 2:

%e ..0..1....1..0....1..1....1..0....0..1....1..0....0..0....1..1....0..1....1..0

%e ..0..1....1..0....0..0....1..0....0..0....1..1....0..1....1..0....1..1....0..0

%e ..0..1....1..0....1..1....0..0....0..0....0..1....0..1....0..0....1..0....0..1

%Y Cf. A185750.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 01 2011