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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.
2

%I #9 Mar 04 2018 06:05:34

%S 14,74,413,2268,12574,69338,383440,2117054,11699556,64620690,

%T 357034452,1972284262,10896200940,60194058786,332543162084,

%U 1837101323030,10149009487404,56067475332178,309742091323076,1711151039052838

%N 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 Column 1 of A205590.

%H R. H. Hardin, <a href="/A205583/b205583.txt">Table of n, a(n) for n = 1..210</a>

%F 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 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 Some solutions for n=4:

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

%e ..1..1....1..2....0..2....0..1....0..1....1..1....1..2....2..2....2..0....2..0

%e ..0..2....0..1....2..0....2..0....2..1....1..1....2..2....1..2....1..0....0..0

%e ..2..2....1..1....0..0....1..0....2..1....1..0....1..0....0..2....2..1....2..1

%e ..1..0....2..0....1..2....0..2....0..1....1..2....1..1....2..2....0..1....2..1

%Y Cf. A205590.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 29 2012