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A184042 1/9 the number of (n+1) X 4 0..2 arrays with all 2 X 2 subblocks having the same four values. 1

%I

%S 25,31,41,61,97,169,305,577,1105,2161,4241,8401,16657,33169,66065,

%T 131857,263185,525841,1050641,2100241,4198417,8394769,16785425,

%U 33566737,67125265,134242321,268468241,536920081,1073807377,2147581969,4295098385

%N 1/9 the number of (n+1) X 4 0..2 arrays with all 2 X 2 subblocks having the same four values.

%C Column 3 of A184048.

%H R. H. Hardin, <a href="/A184042/b184042.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*(25 - 44*x - 52*x^2 + 88*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

%F a(n) = 3*2^(n/2) + 2^(n+1) + 17 for n even.

%F a(n) = 2^(n+1) + 2^((n+3)/2) + 17 for n odd.

%F (End)

%e Some solutions for 5 X 4:

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

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

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

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

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

%Y Cf. A184048.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 08 2011

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Last modified January 27 12:24 EST 2023. Contains 359840 sequences. (Running on oeis4.)