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Number of n-length words over a 6-ary alphabet {a_1,a_2,...,a_6} avoiding consecutive letters a_i, a_{i+1}.
2

%I #8 Oct 26 2016 11:36:19

%S 1,6,31,160,826,4264,22012,113632,586599,3028182,15632291,80698096,

%T 416585304,2150525528,11101591924,57309407232,295846593873,

%U 1527239790702,7884023093755,40699450421136,210101523661770,1084600646648368,5599000626972168,28903549078371648

%N Number of n-length words over a 6-ary alphabet {a_1,a_2,...,a_6} avoiding consecutive letters a_i, a_{i+1}.

%H Alois P. Heinz, <a href="/A277669/b277669.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5,4,-3,2,-1)

%F G.f.: 1/(1 + Sum_{j=1..6} (7-j)*(-x)^j).

%p a:= n-> (<<0|1|0|0|0|0>, <0|0|1|0|0|0>, <0|0|0|1|0|0>,

%p <0|0|0|0|1|0>, <0|0|0|0|0|1>, <-1|2|-3|4|-5|6>>^n)[6$2]:

%p seq(a(n), n=0..30);

%Y Column k=6 of A277666.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Oct 26 2016