login
Number of length-n 0..4 arrays with no repeated value equal to the previous repeated value.
1

%I #8 Jan 22 2019 08:20:58

%S 5,25,120,580,2780,13300,63420,301780,1433180,6795700,32180220,

%T 152216980,719335580,3396714100,16028713020,75595396180,356358069980,

%U 1679206088500,7909957661820,37249421039380,175371521796380,825484323238900

%N Number of length-n 0..4 arrays with no repeated value equal to the previous repeated value.

%H R. H. Hardin, <a href="/A269463/b269463.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 4*a(n-2) - 32*a(n-3).

%F Empirical g.f.: 5*x*(1 - 2*x - 7*x^2) / ((1 - 4*x)*(1 - 3*x - 8*x^2)). - _Colin Barker_, Jan 22 2019

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 4 of A269467.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 27 2016