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Number of length-n 0..6 arrays with no repeated value equal to the previous repeated value.
1

%I #7 Jan 22 2019 08:35:30

%S 7,49,336,2310,15834,108402,741090,5060706,34523202,235304034,

%T 1602555906,10906971810,74188793154,504367206882,3427339028610,

%U 23280526483746,158079249910722,1073053862250594,7281968079533826,49404973360789410

%N Number of length-n 0..6 arrays with no repeated value equal to the previous repeated value.

%H R. H. Hardin, <a href="/A269465/b269465.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 11*a(n-1) -18*a(n-2) -72*a(n-3).

%F Conjectures from _Colin Barker_, Jan 22 2019: (Start)

%F G.f.: 7*x*(1 - 4*x - 11*x^2) / ((1 - 6*x)*(1 - 5*x - 12*x^2)).

%F a(n) = (7/657)*2^(-4-n) * (-73*3^n*4^(1+n) + (949-103*sqrt(73))*(5-sqrt(73))^n + (5+sqrt(73))^n*(949+103*sqrt(73))).

%F (End)

%e Some solutions for n=6:

%e ..4. .4. .2. .4. .4. .4. .5. .4. .3. .0. .6. .5. .0. .4. .2. .1

%e ..5. .4. .2. .1. .2. .4. .6. .0. .2. .6. .4. .2. .6. .0. .4. .1

%e ..3. .5. .4. .4. .2. .2. .6. .0. .1. .0. .0. .0. .6. .6. .6. .0

%e ..6. .2. .3. .3. .4. .6. .0. .6. .0. .5. .4. .0. .3. .0. .0. .5

%e ..3. .1. .5. .6. .2. .5. .3. .2. .5. .3. .1. .4. .6. .5. .3. .3

%e ..5. .6. .0. .4. .0. .4. .2. .4. .1. .1. .1. .6. .0. .5. .3. .3

%Y Column 6 of A269467.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 27 2016