A269489 - OEIS

%I #7 Mar 21 2018 17:19:56

%S 4,16,64,250,964,3680,13946,52562,197288,738190,2755492,10266910,

%T 38201266,141989786,527337242,1957297844,7261528508,26930981728,

%U 99854569606,370173077224,1372098494764,5085413836406,18846930103274

%N Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by one.

%C Column 3 of A269494.

%H R. H. Hardin, <a href="/A269489/b269489.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) - 24*a(n-2) + 9*a(n-3) + 26*a(n-4) + 3*a(n-5).

%F Empirical g.f.: 2*x*(2 - 10*x + 8*x^2 + 11*x^3 + x^4) / ((1 - 3*x)*(1 - 6*x + 6*x^2 + 9*x^3 + x^4)). - _Colin Barker_, Mar 21 2018

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Cf. A269494.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 28 2016