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A251746 9-step Fibonacci sequence starting with 0,0,0,0,0,0,0,1,0.

%I A251746 #27 Mar 28 2025 10:50:12
%S A251746 0,0,0,0,0,0,0,1,0,1,2,4,8,16,32,64,128,255,510,1019,2036,4068,8128,
%T A251746 16240,32448,64832,129536,258817,517124,1033229,2064422,4124776,
%U A251746 8241424,16466608,32900768,65736704,131343872,262428927,524340730,1047648231,2093232040
%N A251746 9-step Fibonacci sequence starting with 0,0,0,0,0,0,0,1,0.
%C A251746 a(n+9) equals the number of n-length binary words avoiding runs of zeros of lengths 9i+8, (i=0,1,2,...). - _Milan Janjic_, Feb 26 2015
%H A251746 Robert Price, <a href="/A251746/b251746.txt">Table of n, a(n) for n = 0..1000</a>
%H A251746 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1,1,1,1).
%F A251746 a(n+9) = a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)+a(n+5)+a(n+6)+a(n+7)+a(n+8).
%F A251746 G.f.: x^7*(x-1)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9) . - _R. J. Mathar_, Mar 28 2025
%F A251746 a(n) = A104144(n+1)-A104144(n). - _R. J. Mathar_, Mar 28 2025
%t A251746 LinearRecurrence[Table[1, {9}], {0, 0, 0, 0, 0, 0, 0, 1, 0}, 44] (* _Michael De Vlieger_, Dec 09 2014 *)
%Y A251746 Other 9-step Fibonacci sequences are A104144, A105755, A127193, A251747, A251748, A251749, A251750, A251751, A251752.
%Y A251746 Cf. A255530 (Indices of primes in this sequence).
%K A251746 nonn,easy
%O A251746 0,11
%A A251746 _Arie Bos_, Dec 07 2014