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%I #18 Feb 14 2018 21:09:45
%S 1,2,4,8,14,24,41,70,120,205,350,597,1018,1736,2960,5047,8605,14671,
%T 25013,42645,72706,123957,211335,360306,614287,1047300,1785545,
%U 3044181,5190033,8848502,15085836,25719884,43849902,74759820,127458225,217303882
%N Number of binary strings of length n with no substrings equal to 0001 or 0110.
%H R. H. Hardin, <a href="/A164396/b164396.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,0,1,-1).
%F a(n) = 2*a(n-1) - a(n-3) + a(n-5) - a(n-6). - _Andrew Howroyd_, Feb 14 2018
%F G.f.: (1 + x^3 - x^5)/((1 - x)*(1 - x - x^2 - x^5)). - _R. J. Mathar_, Nov 30 2011
%t LinearRecurrence[{2,0,-1,0,1,-1}, {1, 2, 4, 8, 14, 24}, 50] (* _G. C. Greubel_, Sep 18 2017 *)
%o (PARI) Vec((1 + x^3 - x^5)/((1 - x)*(1 - x - x^2 - x^5)) + O(x^40)) \\ _G. C. Greubel_, Sep 18 2017
%K nonn
%O 0,2
%A _R. H. Hardin_, Aug 14 2009
%E a(0)-a(3) prepended by _Andrew Howroyd_, Feb 14 2018
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