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%I #7 Jan 24 2019 08:37:19
%S 30,1048,10192,55836,217714,677200,1792788,4205812,8981446,17790024,
%T 33133720,58623628,99312282,162086656,256126684,393434340,589438318,
%U 863679352,1240581216,1750312444,2429743810,3323506608,4485156772
%N Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by other than one.
%H R. H. Hardin, <a href="/A269541/b269541.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 - 12*n^3 + 22*n^2 - 18*n + 4.
%F Conjectures from _Colin Barker_, Jan 24 2019: (Start)
%F G.f.: 2*x*(15 + 404*x + 1324*x^2 + 982*x^3 - 93*x^4 - 88*x^5 - 22*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=3:
%e ..3. .3. .1. .2. .0. .3. .3. .3. .0. .3. .2. .3. .3. .1. .1. .2
%e ..1. .1. .1. .0. .1. .2. .0. .1. .3. .3. .3. .2. .1. .1. .2. .1
%e ..2. .1. .2. .3. .0. .0. .2. .3. .3. .2. .0. .1. .3. .3. .0. .0
%e ..3. .3. .3. .3. .1. .2. .1. .3. .0. .2. .1. .3. .0. .0. .2. .1
%e ..0. .2. .2. .2. .0. .1. .3. .2. .3. .0. .0. .0. .0. .0. .1. .0
%e ..1. .2. .0. .1. .3. .2. .0. .2. .2. .3. .0. .2. .2. .1. .2. .1
%e ..1. .3. .0. .3. .1. .0. .0. .1. .2. .0. .1. .3. .1. .1. .1. .0
%Y Row 7 of A269537.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 29 2016
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