A164395 - OEIS

%I #18 Feb 14 2018 21:09:38

%S 1,2,4,8,14,24,42,72,122,208,354,600,1018,1728,2930,4968,8426,14288,

%T 24226,41080,69658,118112,200274,339592,575818,976368,1655554,2807192,

%U 4759930,8071040,13685426,23205288,39347370,66718224,113128802,191823544

%N Number of binary strings of length n with no substrings equal to 0001 or 0101.

%H R. H. Hardin, <a href="/A164395/b164395.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,-1,2,-2).

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

%F G.f.: (1 + x^2)/((1 - x)*(1 - x - 2*x^3)). - _R. J. Mathar_, Dec 01 2011

%t LinearRecurrence[{2,-1,2,-2}, {1, 2, 4, 8}, 50] (* _G. C. Greubel_, Sep 18 2017 *)

%o (PARI) Vec((1 + x^2)/((1 - x)*(1 - x - 2*x^3)) + O(x^40)) \\ _G. C. Greubel_, Sep 18 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