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A164406 Number of binary strings of length n with no substrings equal to 0011 or 0101. 2

%I

%S 1,2,4,8,14,24,41,68,111,180,289,460,728,1146,1795,2800,4352,6742,

%T 10414,16044,24659,37818,57885,88440,134899,205448,312448,474548,

%U 719861,1090734,1650908,2496260,3770910,5691360,8582653,12932512,19472363,29298540,44053525

%N Number of binary strings of length n with no substrings equal to 0011 or 0101.

%H Alois P. Heinz, <a href="/A164406/b164406.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 (2,-1,2,-2,0,-1).

%F G.f.: (x^2+1)/(x^3+x-1)^2. - _R. J. Mathar_, Nov 30 2011

%F a(n) = Sum_{i=0..floor((n+1)/2)} (n+1-2i) * C(n+1-2i,i). - _Wesley Ivan Hurt_, Nov 17 2017

%t LinearRecurrence[{2,-1,2,-2,0,-1}, {14,24,41,68,111,180}, 50] (* _G. C. Greubel_, Sep 19 2017 *)

%o (PARI) x='x+O('x^50); Vec((x^2+1)/(x^3+x-1)^2) \\ _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_, Oct 27 2017

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Last modified July 4 15:43 EDT 2020. Contains 335448 sequences. (Running on oeis4.)