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%I #26 Jul 03 2021 01:53:24
%S 1,2,4,5,7,11,16,23,34,50,73,107,157,230,337,494,724,1061,1555,2279,
%T 3340,4895,7174,10514,15409,22583,33097,48506,71089,104186,152692,
%U 223781,327967,480659,704440,1032407,1513066,2217506,3249913,4762979,6980485,10230398
%N Number of binary strings of length n with no substrings equal to 000, 001, or 010.
%H Alois P. Heinz, <a href="/A164316/b164316.txt">Table of n, a(n) for n = 0..2000</a> (first 500 terms from R. H. Hardin)
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1).
%F G.f.: -(2*x^2+x+1)/(x^3+x-1). - _R. J. Mathar_, Nov 28 2011
%F a(n) = 4 + Sum_{i=0..n-3} a(i) for n>2. - _Greg Dresden_, Jul 02 2021
%e All solutions for n=6: 101100 101101 101110 101111 011011 011100 011101 011110 011111 111011 110110 110111 111100 111101 111110 111111.
%t LinearRecurrence[{1, 0, 1}, {1, 2, 4}, 80] (* _Vladimir Joseph Stephan Orlovsky_, Feb 15 2012, edited by _Greg Dresden_, Jul 02 2021 *)
%K easy,nonn
%O 0,2
%A _R. H. Hardin_, Aug 12 2009
%E Edited by _Alois P. Heinz_, Oct 11 2017
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