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A269607 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by one or less. 1

%I

%S 8,62,222,572,1220,2298,3962,6392,9792,14390,20438,28212,38012,50162,

%T 65010,82928,104312,129582,159182,193580,233268,278762,330602,389352,

%U 455600,529958,613062,705572,808172,921570,1046498,1183712,1333992

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

%H R. H. Hardin, <a href="/A269607/b269607.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Jan 25 2019: (Start)

%F G.f.: 2*x*(4 + 11*x - 4*x^2 + x^3) / (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=7:

%e ..0. .7. .6. .5. .4. .1. .1. .5. .3. .5. .0. .3. .1. .3. .4. .4

%e ..5. .6. .4. .1. .0. .2. .4. .1. .4. .1. .3. .0. .7. .0. .6. .3

%e ..3. .5. .6. .7. .6. .1. .6. .7. .3. .7. .4. .3. .0. .6. .0. .7

%e ..7. .7. .6. .5. .1. .4. .2. .4. .2. .6. .7. .4. .1. .7. .1. .7

%Y Row 4 of A269606.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 01 2016

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Last modified July 30 04:51 EDT 2021. Contains 346348 sequences. (Running on oeis4.)