A269687 - OEIS

%I #8 Jan 27 2019 18:05:41

%S 6,36,216,1284,7584,44556,260616,1518804,8823984,51132636,295646616,

%T 1706201124,9830779584,56564639916,325076005416,1866287024244,

%U 10704981330384,61356265686396,351432308441016,2011741878388164

%N Number of length-n 0..5 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 5+1.

%H R. H. Hardin, <a href="/A269687/b269687.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 21*a(n-2) - 20*a(n-3).

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

%F G.f.: 6*x*(1 - 4*x - 3*x^2) / ((1 - 5*x)*(1 - 5*x - 4*x^2)).

%F a(n) = (3/205)*2^(-2-n)*(-41*2^(2+n)*5^n-5*(5-sqrt(41))^n*(-41+7*sqrt(41)) + 5*(5+sqrt(41))^n*(41+7*sqrt(41))).

%F (End)

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Column 5 of A269690.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 03 2016