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%I #27 Feb 10 2020 01:36:23
%S 1,2,4,8,13,21,33,50,75,112,166,245,361,531,780,1145,1680,2464,3613,
%T 5297,7765,11382,16683,24452,35838,52525,76981,112823,165352,242337,
%U 355164,520520,762861,1118029,1638553,2401418,3519451,5158008,7559430,11078885,16236897
%N Number of binary strings of length n with no substrings equal to 0000, 0011, or 1011.
%H Alois P. Heinz, <a href="/A164429/b164429.txt">Table of n, a(n) for n = 0..2000</a> (first 500 terms from R. H. Hardin)
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-1).
%F G.f.: (x+1)*(x^2+1)*(x^2-x+1)/((x-1)*(x^3+x-1)). - _R. J. Mathar_, Jan 19 2011
%F a(n) = a(n-1) + a(n-3) + 4 for n>4. - _Greg Dresden_, Feb 09 2020
%t LinearRecurrence[{2, -1, 1, -1}, {1, 2, 4, 8, 13, 21}, 41] (* _Harvey P. Dale_, Sep 02 2017; amended for offset 0 by _Georg Fischer_, Apr 02 2019 *)
%o (PARI) x='x+O('x^50); Vec((x+1)*(x^2+1)*(x^2-x+1)/((x-1)*(x^3+x-1))) \\ _Georg Fischer_, Apr 02 2019
%K nonn,easy
%O 0,2
%A _R. H. Hardin_, Aug 14 2009
%E Edited by _Alois P. Heinz_, Oct 11 2017
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