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%I #36 Feb 18 2020 01:16:10
%S 1,2,4,5,6,7,9,11,13,16,20,24,29,36,44,53,65,80,97,118,145,177,215,
%T 263,322,392,478,585,714,870,1063,1299,1584,1933,2362,2883,3517,4295,
%U 5245,6400,7812,9540,11645,14212,17352,21185,25857,31564,38537,47042,57421
%N Number of binary strings of length n with no substrings equal to 000, 010, or 111.
%H Alois P. Heinz, <a href="/A164317/b164317.txt">Table of n, a(n) for n = 0..5000</a> (first 500 terms from R. H. Hardin)
%H Lukas Fleischer, Jeffrey Shallit, <a href="https://arxiv.org/abs/1911.12464">Words With Few Palindromes, Revisited</a>, arXiv:1911.12464 [cs.FL], 2019.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1).
%F G.f.: -(x^2+x+1)*(x^3+2*x^2+x+1)/(x^4+x^3-1). - _R. J. Mathar_, Nov 28 2011
%e All solutions for N=8
%e 00110110 00110011 10110110 10110011 10011001 10011011 01100110 01101100
%e 01101101 11001100 11001101 11011001 11011011
%t CoefficientList[Series[-(x^2 + x + 1) (x^3 + 2 x^2 + x + 1)/(x^4 + x^3 - 1), {x, 0, 50}], x] (* _Michael De Vlieger_, Feb 17 2020 *)
%K nonn,easy
%O 0,2
%A _R. H. Hardin_, Aug 12 2009
%E Edited by _Alois P. Heinz_, Oct 11 2017
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