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A164402 Number of binary strings of length n with no substrings equal to 0010 or 0110. 1

%I

%S 1,2,4,8,14,24,40,68,116,200,344,592,1016,1744,2992,5136,8816,15136,

%T 25984,44608,76576,131456,225664,387392,665024,1141632,1959808,

%U 3364352,5775488,9914624,17020160,29218048,50157824,86104576,147813376,253747200

%N Number of binary strings of length n with no substrings equal to 0010 or 0110.

%H R. H. Hardin, <a href="/A164402/b164402.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,2)

%F a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4). - _Andrew Howroyd_, Feb 14 2018

%F G.f.: (1 + 2*x^3)/(1 - 2*x + 2*x^3 - 2*x^4). - _R. J. Mathar_, Nov 30 2011

%t LinearRecurrence[{2,0,-2,2}, {1, 2, 4, 8}, 50] ( _G. C. Greubel_, Sep 19 2017 *)

%o (PARI) Vec((1 + 2*x^3)/(1 - 2*x + 2*x^3 - 2*x^4) + O(x^40)) \\ _G. C. Greubel_, Sep 19 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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Last modified April 17 19:51 EDT 2021. Contains 343070 sequences. (Running on oeis4.)