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%I #7 Jan 24 2019 11:45:32
%S 64,659,3680,14239,43184,110339,248464,507935,962144,1713619,2900864,
%T 4705919,7362640,11165699,16480304,23752639,33521024,46427795,
%U 63231904,84822239,112231664,146651779,189448400,242177759,306603424,384713939
%N Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by more than one.
%H R. H. Hardin, <a href="/A269586/b269586.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^6 + 6*n^5 + 9*n^4 + 22*n^3 + 15*n^2 + 12*n - 1.
%F Conjectures from _Colin Barker_, Jan 24 2019: (Start)
%F G.f.: x*(64 + 211*x + 411*x^2 + 78*x^3 - 34*x^4 - 9*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 ..6. .2. .2. .4. .4. .0. .6. .4. .5. .4. .6. .0. .3. .2. .5. .5
%e ..3. .4. .2. .1. .4. .5. .0. .6. .4. .0. .0. .6. .6. .3. .0. .1
%e ..6. .3. .0. .1. .4. .0. .5. .3. .4. .3. .2. .5. .6. .4. .6. .3
%e ..1. .6. .2. .5. .1. .6. .5. .3. .0. .2. .2. .6. .6. .0. .5. .6
%e ..0. .3. .6. .2. .0. .3. .3. .5. .6. .0. .3. .5. .0. .4. .0. .4
%e ..4. .3. .3. .6. .1. .4. .1. .2. .2. .4. .6. .1. .2. .3. .3. .3
%Y Row 6 of A269583.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 01 2016
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