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A205312 Number of (n+1) X 3 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

%I A205312 #8 Jun 11 2018 09:26:18
%S A205312 20,84,376,1708,7784,35500,161928,738636,3369320,15369324,70107976,
%T A205312 319801228,1458790184,6654348460,30354161928,138462112716,
%U A205312 631602239720,2881086973164,13142230386376,59948977985548,273460429154984
%N A205312 Number of (n+1) X 3 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.
%C A205312 Column 2 of A205318.
%H A205312 R. H. Hardin, <a href="/A205312/b205312.txt">Table of n, a(n) for n = 1..210</a>
%F A205312 Empirical: a(n) = 6*a(n-1) -7*a(n-2) +2*a(n-3).
%F A205312 Empirical g.f.: 4*x*(5 - 9*x + 3*x^2) / ((1 - x)*(1 - 5*x + 2*x^2)). - _Colin Barker_, Jun 11 2018
%e A205312 Some solutions for n=4:
%e A205312 ..0..0..0....0..1..0....0..0..1....0..1..1....0..0..1....0..1..0....0..0..1
%e A205312 ..0..0..0....0..1..0....0..1..1....1..1..0....0..1..1....0..0..0....0..1..1
%e A205312 ..0..0..0....0..1..1....1..1..0....1..0..0....0..0..1....1..0..1....0..1..0
%e A205312 ..0..0..0....1..1..0....0..1..0....1..1..1....0..1..1....0..0..1....0..0..0
%e A205312 ..0..0..0....1..0..0....0..0..0....0..0..1....1..1..0....0..1..1....1..0..1
%Y A205312 Cf. A205318.
%K A205312 nonn
%O A205312 1,1
%A A205312 _R. H. Hardin_, Jan 25 2012