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A269496 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by one. 1

%I

%S 24,215,964,3021,7616,16579,32460,58649,99496,160431,248084,370405,

%T 536784,758171,1047196,1418289,1887800,2474119,3197796,4081661,

%U 5150944,6433395,7959404,9762121,11877576,14344799,17205940,20506389,24294896

%N Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by one.

%H R. H. Hardin, <a href="/A269496/b269496.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^5 + 5*n^4 + 10*n^3 + 4*n^2 + 3*n + 1.

%F Conjectures from _Colin Barker_, Jan 23 2019: (Start)

%F G.f.: x*(24 + 71*x + 34*x^2 - 18*x^3 + 10*x^4 - x^5) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6

%F (End)

%e Some solutions for n=6:

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

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

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

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

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

%Y Row 5 of A269494.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 28 2016

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Last modified October 17 00:35 EDT 2021. Contains 348048 sequences. (Running on oeis4.)