%I #22 Oct 12 2017 14:46:36
%S 1,2,4,8,14,25,44,77,134,233,405,703,1220,2117,3673,6372,11054,19176,
%T 33265,57705,100101,173645,301221,522526,906422,1572363,2727565,
%U 4731484,8207665,14237766,24698130,42843633,74320480,128923094,223641776,387949454,672972561
%N Number of binary strings of length n with no substrings equal to 0000 or 0111.
%H Alois P. Heinz, <a href="/A164391/b164391.txt">Table of n, a(n) for n = 0..2000</a> (first 500 terms from R. H. Hardin)
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,0,-1,-1).
%F G.f.: (x+1)*(x^2+1)/((x-1)*(x^5+2*x^4+2*x^3+x^2-1)). - _R. J. Mathar_, Nov 28 2011
%F a(n) = 1.6443631... * 1.7346913...^n + O(1), where 1.7346913... is the real root of x^5 - x^3 - 2x^2 - 2x - 1. [_Charles R Greathouse IV_, Jan 18 2012]
%t LinearRecurrence[{1,1,1,0,-1,-1}, {14, 25, 44, 77, 134, 233}, 50] (* _G. C. Greubel_, Sep 18 2017 *)
%o (PARI) x='x+O('x^50); Vec(x^4*(-14-11*x-5*x^2+6*x^3+12*x^4+8*x^5)/((1-x)*(x^5+2*x^4+2*x^3+ x^2-1))) \\ _G. C. Greubel_, Sep 18 2017
%K nonn,easy
%O 0,2
%A _R. H. Hardin_, Aug 14 2009
%E Conjectured g.f. verified by _Charles R Greathouse IV_, Jan 18 2012
%E Edited by _Alois P. Heinz_, Oct 12 2017