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A251710 7-step Fibonacci sequence starting with (0,0,0,0,0,1,0).

%I A251710 #31 Mar 28 2025 10:29:50
%S A251710 0,0,0,0,0,1,0,1,2,4,8,16,32,63,126,251,500,996,1984,3952,7872,15681,
%T A251710 31236,62221,123942,246888,491792,979632,1951392,3887103,7742970,
%U A251710 15423719,30723496,61200104,121908416,242837200,483723008,963558913,1919374856,3823325993
%N A251710 7-step Fibonacci sequence starting with (0,0,0,0,0,1,0).
%C A251710 a(n+7) equals the number of n-length binary words avoiding runs of zeros of lengths 7i+6, (i=0,1,2,...). - _Milan Janjic_, Feb 26 2015
%H A251710 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1,1).
%F A251710 a(n+7) = a(n) + a(n+1) + a(n+2) + a(n+3) + a(n+4) + a(n+5) + a(n+6).
%F A251710 G.f.: x^5*(x-1)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7) . - _R. J. Mathar_, Mar 28 2025
%F A251710 a(n) = A066178(n-5)-A066178(n-6). - _R. J. Mathar_, Mar 28 2025
%t A251710 LinearRecurrence[Table[1, {7}], {0, 0, 0, 0, 0, 1, 0}, 40] (* _Michael De Vlieger_, Dec 09 2014 *)
%o A251710 (J) NB. see A251713 for the program and apply it to 0 0 0 0 0 1 0.
%Y A251710 Other 7-step Fibonacci sequences are A066178, A104621, A122189, A251711, A251712, A251713, A251714.
%K A251710 nonn,easy
%O A251710 0,9
%A A251710 _Arie Bos_, Dec 07 2014