A269686 - OEIS

%I #8 Jan 27 2019 10:58:55

%S 5,25,125,615,2995,14465,69405,331255,1574195,7454385,35195485,

%T 165766535,779138355,3655796065,17128371485,80151962775,374677320115,

%U 1749902587025,8166591981405,38087874378535,177538468225715,827166275107905

%N Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 4+1.

%H R. H. Hardin, <a href="/A269686/b269686.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 13*a(n-2) - 12*a(n-3).

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

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

%F a(n) =  (-5/42)*(7*4^n + (2-sqrt(7))^n*(-7+3*sqrt(7)) - (2+sqrt(7))^n*(7+3*sqrt(7))).

%F (End)

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 4 of A269690.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 03 2016