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A251759 10-step Fibonacci sequence starting with 0,0,0,0,0,0,0,0,1,0.

%I A251759 #26 Mar 28 2025 11:05:56
%S A251759 0,0,0,0,0,0,0,0,1,0,1,2,4,8,16,32,64,128,256,511,1022,2043,4084,8164,
%T A251759 16320,32624,65216,130368,260608,520960,1041409,2081796,4161549,
%U A251759 8319014,16629864,33243408,66454192,132843168,265555968,530851328,1061181696,2121321983
%N A251759 10-step Fibonacci sequence starting with 0,0,0,0,0,0,0,0,1,0.
%C A251759 a(n+10) equals the number of n-length binary words avoiding runs of zeros of lengths 10i+9, (i=0,1,2,...). - _Milan Janjic_, Feb 26 2015
%H A251759 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1,1,1,1,1).
%F A251759 a(n+10) = 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) +a(n+9).
%F A251759 G.f.: x^8*(x-1)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10) . - _R. J. Mathar_, Mar 28 2025
%F A251759 a(n) = A122265(n+1)-A122265(n). - _R. J. Mathar_, Mar 28 2025
%t A251759 LinearRecurrence[Table[1, {10}], {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, 45] (* _Michael De Vlieger_, Dec 08 2014 *)
%Y A251759 Other 10-step Fibonacci sequences are A251760, A251761, A251762, A251763, A251764, A251765, A251766.
%K A251759 nonn,easy
%O A251759 0,12
%A A251759 _Arie Bos_, Dec 07 2014