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A267905 Number of n X 1 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

%I A267905 #8 Jan 11 2019 09:05:52
%S A267905 1,2,5,13,34,88,225,569,1426,3548,8777,21613,53026,129712,316545,
%T A267905 770993,1874914,4553588,11047625,26779909,64869586,157043368,
%U A267905 380004897,919150313,2222499826,5372538572,12984354185,31374801373,75801065794
%N A267905 Number of n X 1 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.
%H A267905 R. H. Hardin, <a href="/A267905/b267905.txt">Table of n, a(n) for n = 1..210</a>
%F A267905 Empirical: a(n) = 5*a(n-1) -7*a(n-2) +a(n-3) +2*a(n-4).
%F A267905 Conjectures from _Colin Barker_, Jan 11 2019: (Start)
%F A267905 G.f.: x*(1 - 3*x + 2*x^2 + x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x - x^2)).
%F A267905 a(n) = ((1-sqrt(2))^(1+n) + (1+sqrt(2))^(1+n) - 2*(2^n-1)) / 4.
%F A267905 (End)
%e A267905 Some solutions for n=8:
%e A267905 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A267905 ..0....1....1....1....1....1....1....1....1....1....1....1....1....1....1....0
%e A267905 ..1....2....2....0....2....2....2....1....2....0....2....0....2....0....2....0
%e A267905 ..2....2....2....0....1....1....1....1....0....1....0....1....1....0....0....1
%e A267905 ..0....1....2....2....2....1....2....2....0....1....0....2....0....0....0....2
%e A267905 ..1....0....2....0....1....1....1....1....1....1....0....0....2....2....0....1
%e A267905 ..2....2....2....0....2....1....2....0....0....0....1....1....2....0....0....0
%e A267905 ..1....2....2....1....1....1....2....2....2....1....0....1....2....0....2....0
%Y A267905 Column 1 of A267911.
%K A267905 nonn
%O A267905 1,2
%A A267905 _R. H. Hardin_, Jan 22 2016