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%I #28 Oct 27 2017 17:46:27
%S 1,2,4,8,14,25,44,78,137,241,423,743,1304,2289,4017,7050,12372,21712,
%T 38102,66865,117340,205918,361361,634145,1112847,1952911,3427120,
%U 6014177,10554145,18521234,32502500,57037912,100094558,175653705,308250764,540942382
%N Number of binary strings of length n with no substrings equal to 0001 or 0010.
%C Nonnegative walks with n steps on the x-axis starting at the origin using steps {1,0,-1} and visiting no point more than twice. Note: a 0 step counts as a visit and a step but does not contribute to the length of the walk. - _David Scambler_, May 22 2012
%H Alois P. Heinz, <a href="/A164392/b164392.txt">Table of n, a(n) for n = 0..2000</a> (first 500 terms from R. H. Hardin)
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -1, 1, -1).
%F From _David Scambler_, May 22 2012: (Start)
%F G.f.: (1+x^3-x^4)/(1-2*x+x^3-x^4+x^5).
%F a(n) = 2^n for n<4; otherwise, a(n) = a(n-1)+a(n-2)+a(n-4)+1. (End)
%t CoefficientList[Series[ (1+x^3-x^4)/(1-2*x+x^3-x^4+x^5) , {x, 0, 45}], x] (* _David Scambler_, May 22 2012 *)
%o (PARI) x='x+O('x^50); Vec( (1+x^3-x^4)/(1-2*x+x^3-x^4+x^5) ) \\ _G. C. Greubel_, sep 18 2017
%Y Cf. A212584, A212585, A212586, A212587, A212589.
%K nonn,easy,walk
%O 0,2
%A _R. H. Hardin_, Aug 14 2009
%E Edited by _Alois P. Heinz_, Oct 27 2017
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