A269685 - OEIS

%I #8 Jan 27 2019 07:52:36

%S 4,16,64,248,944,3544,13168,48536,177776,647896,2351728,8508440,

%T 30701168,110537560,397266544,1425629336,5109684848,18295104472,

%U 65449056880,233970500888,835908980336,2984966034520,10654610339440,38017445912984

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

%H R. H. Hardin, <a href="/A269685/b269685.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 7*a(n-2) - 6*a(n-3).

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

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

%F a(n) = 2^(-n)*(-17*2^(2+n)*3^n + (51-15*sqrt(17))*(3-sqrt(17))^n + 3*(3+sqrt(17))^n*(17+5*sqrt(17))) / 51.

%F (End)

%e Some solutions for n=9:

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

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

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

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

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

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

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

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

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

%Y Column 3 of A269690.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 03 2016