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%I #22 Apr 02 2019 17:05:41
%S 1,2,4,8,14,25,45,81,145,260,467,838,1503,2697,4840,8684,15581,27958,
%T 50166,90012,161509,289799,519989,933019,1674126,3003903,5389930,
%U 9671201,17353133,31136896,55869228,100246695,179873620,322748972,579111590,1039105525
%N Number of binary strings of length n with no substrings equal to 0000 or 0101.
%H Alois P. Heinz, <a href="/A164389/b164389.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 (1,0,2,1)
%F G.f.: -(x+1)*(x^2+1)^2/(x^4+2*x^3+x-1). - _R. J. Mathar_, Dec 01 2011
%t LinearRecurrence[{1, 0, 2, 1}, {1, 2, 4, 8, 14, 25}, 50] (* _G. C. Greubel_, Sep 18 2017; amended for offset 0 by _Georg Fischer_, Apr 02 2019 *)
%o (PARI) x='x+O('x^50); Vec(((x+1)*(x^2+1)^2)/(1-x-2*x^3-x^4)) \\ _G. C. Greubel_, Sep 18 2017; amended for offset 0 by _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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