A269538 - OEIS

%I #7 Jan 24 2019 08:21:08

%S 10,64,222,568,1210,2280,3934,6352,9738,14320,20350,28104,37882,50008,

%T 64830,82720,104074,129312,158878,193240,232890,278344,330142,388848,

%U 455050,529360,612414,704872,807418,920760,1045630,1182784,1333002

%N Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than one.

%H R. H. Hardin, <a href="/A269538/b269538.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^4 + 4*n^3 + 3*n^2 + 2*n.

%F Conjectures from _Colin Barker_, Jan 24 2019: (Start)

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

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=3:

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

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

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

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

%Y Row 4 of A269537.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 29 2016