A164409 - OEIS

%I #20 Apr 04 2024 04:22:37

%S 13,22,39,69,121,212,372,653,1146,2011,3529,6193,10868,19072,33469,

%T 58734,103071,180877,317417,557028,977516,1715421,3010354,5282803,

%U 9270673,16268897,28549924,50101624,87922221,154292742,270764887,475159253

%N Number of binary strings of length n with no substrings equal to 0000 0001 or 0100.

%H R. H. Hardin, <a href="/A164409/b164409.txt">Table of n, a(n) for n=4..500</a>

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

%F G.f.: x^4*(13-4*x+8*x^2)/(1-2*x+x^2-x^3). - _R. J. Mathar_, Nov 30 2011

%t LinearRecurrence[{2,-1,1}, {13, 22, 39}, 50] (* _G. C. Greubel_, Sep 19 2017 *)

%o (PARI) my(x='x+O('x^50)); Vec(x^4*(13-4*x+8*x^2)/(1-2*x+x^2-x^3)) \\ _G. C. Greubel_, Sep 19 2017

%K nonn,easy

%O 4,1

%A _R. H. Hardin_, Aug 14 2009