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%I #33 Sep 08 2022 08:45:47
%S 1,2,4,8,14,24,41,68,112,184,300,488,793,1286,2084,3376,5466,8848,
%T 14321,23176,37504,60688,98200,158896,257105,416010,673124,1089144,
%U 1762278,2851432,4613721,7465164,12078896,19544072,31622980,51167064,82790057,133957134
%N Number of binary strings of length n with no substrings equal to 0001 or 0111.
%H Alois P. Heinz, <a href="/A164397/b164397.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 (2,0,0,-2,0,1).
%F G.f.: -1/((x^2+x+1)*(x^2+x-1)*(x-1)^2). - _R. J. Mathar_, Nov 30 2011
%t LinearRecurrence[{2,0,0,-2,0,1},{14,24,41,68,112,184},40] (* _Harvey P. Dale_, Jan 23 2012 *)
%t CoefficientList[Series[-1 (14 - 4 x - 7 x^2 - 14 x^3 + 4 x^4 + 8 x^5) / ((1 + x + x^2) (x^2 + x - 1) (x - 1)^2), {x, 0, 33}], x] (* _Vincenzo Librandi_, Sep 19 2017 *)
%o (PARI) x='x+O('x^50); Vec(-x^4*(14-4*x-7*x^2-14*x^3+4*x^4+8*x^5)/( (1+x+x^2)*(x^2+x-1)*(x-1)^2 )) \\ _G. C. Greubel_, Sep 18 2017
%o (Magma) I:=[14,24,41,68,112,184]; [n le 6 select I[n] else 2*Self(n-1)-2*Self(n-4)+Self(n-6): n in [1..40]]; // _Vincenzo Librandi_, Sep 19 2017
%Y Cf. A178982.
%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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