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A269635 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1. 1

%I #7 Jan 25 2019 09:28:34

%S 4,16,60,221,796,2828,9928,34537,119236,409098,1396288,4744671,

%T 16062116,54199810,182382428,612236251,2050883956,6857469364,

%U 22892085300,76311433969,254067536796,844941922160,2807225267056,9318543171653

%N Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

%H R. H. Hardin, <a href="/A269635/b269635.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) - 21*a(n-2) - 19*a(n-3) + 93*a(n-4) + 27*a(n-5) - 133*a(n-6) - 87*a(n-7).

%F Empirical g.f.: x*(4 - 20*x + 93*x^3 - x^4 - 151*x^5 - 89*x^6) / ((1 - 3*x)*(1 - 6*x + 3*x^2 + 28*x^3 - 9*x^4 - 54*x^5 - 29*x^6)). - _Colin Barker_, Jan 25 2019

%e Some solutions for n=9:

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

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

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

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

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

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

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

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

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

%Y Column 3 of A269640.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 02 2016

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