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Number of length-6 0..n arrays with no repeated value greater than or equal to the previous repeated value.
1

%I #8 Jan 21 2019 12:22:35

%S 16,394,2872,12380,39560,104006,238224,492312,939360,1681570,2857096,

%T 4647604,7286552,11068190,16357280,23599536,33332784,46198842,

%U 62956120,84492940,111841576,146193014,188912432,241555400,305884800,383888466

%N Number of length-6 0..n arrays with no repeated value greater than or equal to the previous repeated value.

%H R. H. Hardin, <a href="/A269412/b269412.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^6 + 6*n^5 + 8*n^4 + (5/3)*n^3 - n^2 + (1/3)*n.

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

%F G.f.: 2*x*(8 + 141*x + 225*x^2 - 5*x^3 - 9*x^4) / (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 ..3. .2. .5. .5. .1. .3. .3. .2. .5. .4. .1. .5. .0. .5. .2. .3

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

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

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

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

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

%Y Row 6 of A269409.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 25 2016