%I #8 Jan 27 2019 16:01:39
%S 7,49,343,2387,16541,114205,786079,5396363,36961757,252671461,
%T 1724352175,11750558099,79971635933,543661764877,3692303721631,
%U 25054980870395,169888502127869,1151188506903253,7796069090763247,52769330311322051
%N Number of length-n 0..6 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 6+1.
%H R. H. Hardin, <a href="/A269688/b269688.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 12*a(n-1) - 31*a(n-2) - 30*a(n-3).
%F Conjectures from _Colin Barker_, Jan 27 2019: (Start)
%F G.f.: 7*x*(1 - 5*x - 4*x^2) / ((1 - 6*x)*(1 - 6*x - 5*x^2)).
%F a(n) = (-7*2^(1+n)*3^n + (21-6*sqrt(14))*(3-sqrt(14))^n + 3*(3+sqrt(14))^n*(7+2*sqrt(14))) / 30.
%F (End)
%e Some solutions for n=6:
%e ..3. .6. .4. .6. .6. .3. .4. .0. .6. .4. .3. .3. .0. .1. .2. .4
%e ..4. .0. .1. .0. .4. .3. .2. .6. .3. .4. .0. .1. .6. .3. .2. .6
%e ..5. .0. .3. .2. .4. .2. .5. .6. .5. .2. .3. .6. .4. .0. .4. .3
%e ..3. .1. .3. .4. .4. .1. .4. .1. .5. .1. .1. .1. .4. .5. .0. .2
%e ..4. .5. .6. .1. .3. .1. .4. .0. .6. .0. .6. .2. .2. .0. .5. .6
%e ..0. .4. .1. .3. .1. .6. .5. .5. .3. .1. .2. .2. .6. .4. .0. .1
%Y Column 6 of A269690.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 03 2016