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%I #14 Feb 12 2023 16:25:24
%S 8,64,512,4096,32768,262144,2097152,16777215,134217712,1073741632,
%T 8589932544,68719456256,549755617280,4398044676096,35184355311616,
%U 281474825715713,2251798471507992,18014386698322304,144115084996645888,1152920611253710848,9223364340274069504
%N Number of 0..7 arrays of length n avoiding the consecutive pattern 0..7.
%C Column 7 of A206455.
%H R. H. Hardin, <a href="/A206454/b206454.txt">Table of n, a(n) for n = 1..210</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,0,0,0,0,0,0,-1).
%F a(n) = 8*a(n-1) - a(n-8).
%F a(n) = Sum_{i=0..floor(n/8)} (-1)^i*8^(n-8*i)*binomial(n-7*i,i).
%F G.f.: x*(8 - x^7) / (1 - 8*x + x^8). - _Colin Barker_, Jun 16 2018
%t Table[Sum[(-1)^i*8^(n-8*i)*Binomial[n-7*i,i],{i,0,Floor[n/8]}],{n,20}] (* _Stefano Spezia_, Feb 12 2023 *)
%Y Cf. A206455.
%K nonn,easy
%O 1,1
%A _R. H. Hardin_, Feb 07 2012
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