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 A269410 Number of length-4 0..n arrays with no repeated value greater than or equal to the previous repeated value. 1

%I

%S 9,63,222,570,1215,2289,3948,6372,9765,14355,20394,28158,37947,50085,

%T 64920,82824,104193,129447,159030,193410,233079,278553,330372,389100,

%U 455325,529659,612738,705222,807795,921165,1046064,1183248,1333497

%N Number of length-4 0..n arrays with no repeated value greater than or equal to the previous repeated value.

%H R. H. Hardin, <a href="/A269410/b269410.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^4 + 4*n^3 + (7/2)*n^2 + (1/2)*n.

%F Conjectures from _Colin Barker_, Jan 21 2019: (Start)

%F G.f.: 3*x*(3 + 6*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=8:

%e ..8. .3. .1. .0. .3. .0. .8. .2. .3. .1. .0. .4. .3. .5. .4. .6

%e ..8. .8. .3. .5. .4. .2. .1. .4. .0. .5. .2. .4. .0. .6. .4. .8

%e ..4. .7. .3. .8. .7. .2. .0. .5. .3. .3. .7. .0. .0. .1. .2. .0

%e ..0. .8. .8. .7. .5. .8. .5. .8. .2. .8. .0. .0. .2. .1. .4. .2

%Y Row 4 of A269409.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 25 2016

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Last modified December 5 20:31 EST 2021. Contains 349558 sequences. (Running on oeis4.)