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 A184032 1/16 the number of (n+1) X 3 0..3 arrays with all 2 X 2 subblocks having the same four values. 1

%I #8 Apr 10 2018 04:52:31

%S 28,40,61,103,181,337,637,1237,2413,4765,9421,18733,37261,74317,

%T 148237,296077,591373,1181965,2362381,4723213,9443341,18883597,

%U 37761037,75515917,151019533,302026765,604028941,1208033293,2416017421,4831985677

%N 1/16 the number of (n+1) X 3 0..3 arrays with all 2 X 2 subblocks having the same four values.

%C Column 2 of A184039.

%H R. H. Hardin, <a href="/A184032/b184032.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*(28 - 44*x - 59*x^2 + 88*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

%F a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 13 for n even.

%F a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 13 for n odd.

%F (End)

%e Some solutions for 5 X 3:

%e ..1..2..1....0..1..0....0..1..0....1..3..1....2..1..2....3..2..3....3..2..3

%e ..0..1..0....2..3..2....1..0..1....1..0..1....3..0..3....0..3..0....2..3..2

%e ..2..1..2....0..1..0....0..1..0....3..1..3....2..1..2....3..2..3....2..3..2

%e ..0..1..0....3..2..3....0..1..0....0..1..0....3..0..3....3..0..3....2..3..2

%e ..2..1..2....1..0..1....0..1..0....1..3..1....1..2..1....2..3..2....2..3..2

%Y Cf. A184039.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 08 2011

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Last modified December 6 09:02 EST 2023. Contains 367600 sequences. (Running on oeis4.)