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 A269436 Number of length-4 0..n arrays with no repeated value greater than the previous repeated value. 1

%I #8 Jan 22 2019 07:46:26

%S 15,78,250,615,1281,2380,4068,6525,9955,14586,20670,28483,38325,50520,

%T 65416,83385,104823,130150,159810,194271,234025,279588,331500,390325,

%U 456651,531090,614278,706875,809565,923056,1048080,1185393,1335775

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

%H R. H. Hardin, <a href="/A269436/b269436.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^4 + 4*n^3 + (11/2)*n^2 + (7/2)*n + 1.

%F Conjectures from _Colin Barker_, Jan 22 2019: (Start)

%F G.f.: x*(15 + 3*x + 10*x^2 - 5*x^3 + x^4) / (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 ..7. .8. .1. .4. .8. .5. .6. .6. .7. .0. .7. .7. .8. .5. .5. .0

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

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

%e ..7. .2. .7. .0. .2. .1. .3. .4. .0. .8. .4. .6. .5. .0. .8. .1

%Y Row 4 of A269435.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 26 2016

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Last modified December 9 03:28 EST 2023. Contains 367681 sequences. (Running on oeis4.)