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A251672 8-step Fibonacci sequence starting with 0,0,0,0,0,0,1,0.

%I A251672 #39 Mar 28 2025 10:15:57
%S A251672 0,0,0,0,0,0,1,0,1,2,4,8,16,32,64,127,254,507,1012,2020,4032,8048,
%T A251672 16064,32064,64001,127748,254989,508966,1015912,2027792,4047536,
%U A251672 8079008,16125952,32187903,64248058,128241127,255973288,510930664,1019833536,2035619536
%N A251672 8-step Fibonacci sequence starting with 0,0,0,0,0,0,1,0.
%C A251672 a(n+8) equals the number of n-length binary words avoiding runs of 0's of lengths 8i+7, (i=0,1,2,...). - _Milan Janjic_, Feb 26 2015
%H A251672 G. C. Greubel, <a href="/A251672/b251672.txt">Table of n, a(n) for n = 0..1000</a>
%H A251672 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1,1,1).
%F A251672 a(n+8) = a(n) +a(n+1) +a(n+2) +a(n+3) +a(n+4) +a(n+5) +a(n+6) +a(n+7).
%F A251672 G.f.: x^6*(x-1)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8) . - _R. J. Mathar_, Mar 28 2025
%F A251672 a(n) = A079262(n+1)-A079262(n). - _R. J. Mathar_, Mar 28 2025
%t A251672 LinearRecurrence[Table[1, {8}], {0, 0, 0, 0, 0, 0, 1, 0}, 43] (* _Michael De Vlieger_, Dec 09 2014 *)
%Y A251672 Other 8-step Fibonacci sequences are A079262, A105754, A251740, A251741, A251742, A251744, A251745.
%K A251672 nonn,easy
%O A251672 0,10
%A A251672 _Arie Bos_, Dec 06 2014