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A277671 Number of n-length words over an 8-ary alphabet {a_1,a_2,...,a_8} avoiding consecutive letters a_i, a_{i+1}.

%I A277671 #11 May 15 2018 13:56:25
%S A277671 1,8,57,406,2892,20600,146736,1045216,7445184,53032832,377758463,
%T A277671 2690813426,19166948203,136528196220,972504760052,6927254109472,
%U A277671 49343562590512,351479407373632,2503624937520704,17833584831080448,127030508108889857,904851724611169300
%N A277671 Number of n-length words over an 8-ary alphabet {a_1,a_2,...,a_8} avoiding consecutive letters a_i, a_{i+1}.
%H A277671 Alois P. Heinz, <a href="/A277671/b277671.txt">Table of n, a(n) for n = 0..1000</a>
%H A277671 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7,6,-5,4,-3,2,-1)
%F A277671 G.f.: 1/(1 + Sum_{j=1..8} (9-j)*(-x)^j).
%p A277671 a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
%p A277671       -add((-1)^j*(9-j)*a(n-j), j=1..8)))
%p A277671     end:
%p A277671 seq(a(n), n=0..25);
%t A277671 LinearRecurrence[{8,-7,6,-5,4,-3,2,-1},{1,8,57,406,2892,20600,146736,1045216},30] (* _Harvey P. Dale_, May 15 2018 *)
%Y A277671 Column k=8 of A277666.
%K A277671 nonn,easy
%O A277671 0,2
%A A277671 _Alois P. Heinz_, Oct 26 2016