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A184368 1/3 the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically. 2

%I

%S 21,153,1107,8019,58077,420633,3046491,22064643,159806277,1157419449,

%T 8382773187,60713414163,439725443661,3184773389433,23066169329547,

%U 167059976482179,1209955382858997,8763272085493593,63469230958692531

%N 1/3 the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.

%C Column 1 of A184376.

%H R. H. Hardin, <a href="/A184368/b184368.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 6*a(n-1) + 9*a(n-2).

%F Conjectures from _Colin Barker_, Feb 27 2018: (Start)

%F G.f.: 3*x*(7 + 9*x) / (1 - 6*x - 9*x^2).

%F a(n) = ((3-3*sqrt(2))^n*(-4+3*sqrt(2)) + (3*(1+sqrt(2)))^n*(4+3*sqrt(2))) / (2*sqrt(2)).

%F (End)

%e Some solutions for 3 X 2 with a(1,1)=0:

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

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

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

%Y Cf. A184376.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 12 2011

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Last modified January 26 17:30 EST 2023. Contains 359833 sequences. (Running on oeis4.)