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 A184045 1/9 the number of (n+1) X 7 0..2 arrays with all 2 X 2 subblocks having the same four values. 1

%I

%S 153,159,169,189,225,297,433,705,1233,2289,4369,8529,16785,33297,

%T 66193,131985,263313,525969,1050769,2100369,4198545,8394897,16785553,

%U 33566865,67125393,134242449,268468369,536920209,1073807505,2147582097,4295098513

%N 1/9 the number of (n+1) X 7 0..2 arrays with all 2 X 2 subblocks having the same four values.

%C Column 6 of A184048.

%H R. H. Hardin, <a href="/A184045/b184045.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).

%F Conjectures from _Colin Barker_, Apr 10 2018: (Start)

%F G.f.: x*(153 - 300*x - 308*x^2 + 600*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

%F a(n) = 3*2^(n/2) + 2^(n+1) + 145 for n even.

%F a(n) = 2^(n+1) + 2^((n+3)/2) + 145 for n odd.

%F (End)

%e Some solutions for 5 X 7:

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

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

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

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

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

%Y Cf. A184048.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 08 2011

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Last modified March 30 13:38 EDT 2023. Contains 361621 sequences. (Running on oeis4.)