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A269610 Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by one or less. 1

%I

%S 14,902,10192,58280,229754,714874,1886252,4405772,9366790,18476654,

%T 34284584,60459952,102126002,166254050,262123204,401850644,600997502,

%U 879255382,1261218560,1777246904,2464424554,3367619402,4540648412

%N Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by one or less.

%H R. H. Hardin, <a href="/A269610/b269610.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^7 + 7*n^6 + 16*n^5 - 12*n^4 - 5*n^3 + 18*n^2 - 15*n + 4.

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

%F G.f.: 2*x*(7 + 395*x + 1684*x^2 + 608*x^3 - 321*x^4 + 143*x^5 + 6*x^6 - 2*x^7) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

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

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

%Y Row 7 of A269606.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 01 2016

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Last modified June 21 19:59 EDT 2021. Contains 345365 sequences. (Running on oeis4.)