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A205583 Number of (n+1) X 2 0..2 arrays with no 2 X 2 subblock having the same number of equal edges as its horizontal or vertical neighbors, and new values 0..2 introduced in row major order.

%I A205583 #9 Mar 04 2018 06:05:34
%S A205583 14,74,413,2268,12574,69338,383440,2117054,11699556,64620690,
%T A205583 357034452,1972284262,10896200940,60194058786,332543162084,
%U A205583 1837101323030,10149009487404,56067475332178,309742091323076,1711151039052838
%N A205583 Number of (n+1) X 2 0..2 arrays with no 2 X 2 subblock having the same number of equal edges as its horizontal or vertical neighbors, and new values 0..2 introduced in row major order.
%C A205583 Column 1 of A205590.
%H A205583 R. H. Hardin, <a href="/A205583/b205583.txt">Table of n, a(n) for n = 1..210</a>
%F A205583 Empirical: a(n) = 21*a(n-2) + 44*a(n-3) + 50*a(n-4) + 12*a(n-5) - 144*a(n-6) for n>7.
%F A205583 Empirical g.f.: x*(14 + 74*x + 119*x^2 + 98*x^3 - 55*x^4 - 330*x^5 + 72*x^6) / (1 - 21*x^2 - 44*x^3 - 50*x^4 - 12*x^5 + 144*x^6). - _Colin Barker_, Mar 04 2018
%e A205583 Some solutions for n=4:
%e A205583 ..0..1....0..0....0..1....0..0....0..0....0..0....0..0....0..1....0..1....0..1
%e A205583 ..1..1....1..2....0..2....0..1....0..1....1..1....1..2....2..2....2..0....2..0
%e A205583 ..0..2....0..1....2..0....2..0....2..1....1..1....2..2....1..2....1..0....0..0
%e A205583 ..2..2....1..1....0..0....1..0....2..1....1..0....1..0....0..2....2..1....2..1
%e A205583 ..1..0....2..0....1..2....0..2....0..1....1..2....1..1....2..2....0..1....2..1
%Y A205583 Cf. A205590.
%K A205583 nonn
%O A205583 1,1
%A A205583 _R. H. Hardin_, Jan 29 2012