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A269609 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by one or less. 1

%I

%S 12,376,2878,12570,40288,105892,242226,499798,952180,1702128,2888422,

%T 4693426,7351368,11157340,16477018,23757102,33536476,46458088,

%U 63281550,84896458,112336432,146793876,189635458,242418310,306906948,385090912

%N Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by one or less.

%H R. H. Hardin, <a href="/A269609/b269609.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^6 + 6*n^5 + 11*n^4 - 8*n^3 + n^2 + 3*n - 2.

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

%F G.f.: 2*x*(6 + 146*x + 249*x^2 - 50*x^3 - 2*x^4 + 12*x^5 - x^6) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

%F (End)

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Row 6 of A269606.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 01 2016

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Last modified July 23 12:19 EDT 2021. Contains 346259 sequences. (Running on oeis4.)