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A269673 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 3+1. 1

%I #8 Jan 26 2019 04:26:21

%S 4,16,60,224,820,2976,10700,38224,135780,480176,1691740,5941824,

%T 20814740,72755776,253836780,884207024,3075861700,10687549776,

%U 37098781820,128668433824,445930140660,1544500542176,5346546062860,18499277662224

%N Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 3+1.

%H R. H. Hardin, <a href="/A269673/b269673.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - a(n-2) - 15*a(n-3).

%F Conjectures from _Colin Barker_, Jan 26 2019: (Start)

%F G.f.: 4*x*(1 - x - 4*x^2) / ((1 - 3*x)*(1 - 2*x - 5*x^2)).

%F a(n) = (-20*3^n + (18-7*sqrt(6))*(1-sqrt(6))^n + (1+sqrt(6))^n*(18+7*sqrt(6))) / 15.

%F (End)

%e Some solutions for n=9:

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

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

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

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

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

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

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

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

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

%Y Column 3 of A269678.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 03 2016

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