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A184035 1/16 the number of (n+1) X 6 0..3 arrays with all 2 X 2 subblocks having the same four values. 1

%I #8 Apr 10 2018 05:56:47

%S 169,181,202,244,322,478,778,1378,2554,4906,9562,18874,37402,74458,

%T 148378,296218,591514,1182106,2362522,4723354,9443482,18883738,

%U 37761178,75516058,151019674,302026906,604029082,1208033434,2416017562,4831985818

%N 1/16 the number of (n+1) X 6 0..3 arrays with all 2 X 2 subblocks having the same four values.

%C Column 5 of A184039.

%H R. H. Hardin, <a href="/A184035/b184035.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*(169 - 326*x - 341*x^2 + 652*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

%F a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 154 for n even.

%F a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 154 for n odd.

%F (End)

%e Some solutions for 3 X 6:

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

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

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

%Y Cf. A184039.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 08 2011

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Last modified February 29 09:21 EST 2024. Contains 370418 sequences. (Running on oeis4.)