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Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 2+1.
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%I #8 Jan 27 2019 07:51:53

%S 3,9,27,75,201,525,1347,3411,8553,21285,52659,129675,318153,778269,

%T 1899267,4625955,11249481,27321525,66285747,160679451,389217513,

%U 942260205,2280029379,5514901875,13334998953,32235231429,77906125107

%N Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 2+1.

%H R. H. Hardin, <a href="/A269684/b269684.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - 2*a(n-3).

%F Conjectures from _Colin Barker_, Jan 27 2019: (Start)

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

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

%F (End)

%e Some solutions for n=9:

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

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

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

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

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

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

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

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

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

%Y Column 2 of A269690.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 03 2016