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A268943 Number of length-n 0..7 arrays with no repeated value unequal to the previous repeated value plus one mod 7+1.

%I A268943 #8 Jan 17 2019 04:20:36
%S A268943 8,64,504,3928,30344,232696,1773384,13443064,101433800,762265720,
%T A268943 5707893576,42605289208,317113497800,2354253598072,17437541654088,
%U A268943 128885063291896,950791205063624,7001691181273720,51477520840048968
%N A268943 Number of length-n 0..7 arrays with no repeated value unequal to the previous repeated value plus one mod 7+1.
%H A268943 R. H. Hardin, <a href="/A268943/b268943.txt">Table of n, a(n) for n = 1..210</a>
%F A268943 Empirical: a(n) = 13*a(n-1) - 34*a(n-2) - 56*a(n-3).
%F A268943 Conjectures from _Colin Barker_, Jan 17 2019: (Start)
%F A268943 G.f.: 8*x*(1 - 5*x - 7*x^2) / ((1 - 7*x)*(1 - 6*x - 8*x^2)).
%F A268943 a(n) = (-272*7^n + (153-37*sqrt(17))*(3-sqrt(17))^n + (3+sqrt(17))^n*(153+37*sqrt(17))) / 34.
%F A268943 (End)
%e A268943 Some solutions for n=5:
%e A268943 ..0. .7. .3. .6. .2. .5. .7. .0. .1. .2. .2. .0. .6. .3. .5. .7
%e A268943 ..7. .6. .5. .7. .1. .2. .7. .5. .1. .1. .4. .5. .4. .3. .5. .5
%e A268943 ..2. .3. .5. .6. .0. .0. .3. .5. .2. .3. .7. .2. .3. .1. .2. .6
%e A268943 ..1. .2. .0. .5. .3. .7. .5. .1. .0. .5. .5. .4. .5. .5. .5. .1
%e A268943 ..1. .0. .3. .3. .3. .0. .6. .5. .7. .1. .3. .4. .4. .6. .4. .6
%Y A268943 Column 7 of A268944.
%K A268943 nonn
%O A268943 1,1
%A A268943 _R. H. Hardin_, Feb 16 2016