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A164480 Number of binary strings of length n with no substrings equal to 0001, 0110 or 1100. 1

%I

%S 1,2,4,8,13,21,34,55,88,142,229,370,598,967,1564,2530,4093,6622,10714,

%T 17335,28048,45382,73429,118810,192238,311047,503284,814330,1317613,

%U 2131942,3449554,5581495,9031048,14612542,23643589,38256130,61899718,100155847

%N Number of binary strings of length n with no substrings equal to 0001, 0110 or 1100.

%H Alois P. Heinz, <a href="/A164480/b164480.txt">Table of n, a(n) for n = 0..2000</a> (first 500 terms from R. H. Hardin)

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).

%F From _Colin Barker_, Oct 27 2017: (Start)

%F G.f.: -(x^8+x^5+x^4-x^3-1)/((x-1)*(x^2+x-1)).

%F a(n) = 2*a(n-1) - a(n-3) for n>6.

%F (End)

%F a(n) = 3*Lucas(n-1) + 1 for n >= 6. - _Greg Dresden_, Oct 10 2020

%o (PARI) Vec(-(x^8+x^5+x^4-x^3-1)/((x-1)*(x^2+x-1)) + O(x^60)) \\ _Colin Barker_, Oct 27 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 April 18 15:54 EDT 2021. Contains 343089 sequences. (Running on oeis4.)