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%I #24 Dec 30 2023 21:19:25
%S 1,2,4,8,13,23,40,68,118,203,349,602,1036,1784,3073,5291,9112,15692,
%T 27022,46535,80137,138002,237652,409256,704773,1213679,2090056,
%U 3599252,6198214,10673843,18381253,31654058,54510940,93872408,161656153,278385443,479403064
%N Number of binary strings of length n with no substrings equal to 0000 0001 or 0011.
%H Alois P. Heinz, <a href="/A164408/b164408.txt">Table of n, a(n) for n = 0..2000</a> (500 terms from R. H. Hardin)
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,-1).
%F G.f.: (x+1)*(x^2+1) / ( 1-x-x^2-x^3+x^4 ). - _R. J. Mathar_, Nov 28 2011
%t CoefficientList[Series[(13 + 10*x + 4*x^2 - 8*x^3)/(1 - x - x^2 - x^3 + x^4), {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Jan 10 2017 *)
%t LinearRecurrence[{1,1,1,-1}, {13, 23, 40, 68}, 50] (* _G. C. Greubel_, Sep 19 2017 *)
%o (PARI) x='x+O('x^50); Vec(x^4*(13+10*x+4*x^2-8*x^3)/(1-x-x^2-x^3+x^4)) \\ _G. C. Greubel_, Sep 19 2017
%K nonn,easy
%O 0,2
%A _R. H. Hardin_, Aug 14 2009
%E Edited by _Alois P. Heinz_, Dec 30 2023
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