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Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than one.
1

%I #8 Jan 23 2019 18:28:04

%S 5,25,120,568,2648,12214,55836,253418,1143256,5131592,22934652,

%T 102124670,453300160,2006497722,8860136576,39040820448,171705037456,

%U 753921273870,3305432501828,14473039186090,63296720868120,276532411704016

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

%H R. H. Hardin, <a href="/A269533/b269533.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 14*a(n-1) - 65*a(n-2) + 80*a(n-3) + 163*a(n-4) - 280*a(n-5) - 208*a(n-6).

%F Empirical g.f.: x*(5 - 45*x + 95*x^2 + 113*x^3 - 319*x^4 - 213*x^5) / ((1 - 4*x)^2*(1 - 6*x + x^2 + 24*x^3 + 13*x^4)). - _Colin Barker_, Jan 23 2019

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 4 of A269537.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 29 2016