A164405 - OEIS

%I #21 Feb 14 2018 21:10:08

%S 1,2,4,8,14,24,41,70,120,207,358,620,1074,1860,3220,5573,9644,16688,

%T 28877,49970,86472,149640,258954,448124,775485,1341986,2322320,

%U 4018795,6954558,12034920,20826530,36040488,62368376,107929017,186772104,323210752

%N Number of binary strings of length n with no substrings equal to 0010 or 1100.

%H R. H. Hardin, <a href="/A164405/b164405.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,0,0,1).

%F a(n) = 2*a(n-1) - a(n-3) + a(n-6). - _Andrew Howroyd_, Feb 14 2018

%F G.f.: (1 + x^3)/(1 - 2*x + x^3 - x^6). - _R. J. Mathar_, Nov 30 2011

%p f:= gfun:-rectoproc({a(n) = 2*a(n-1)-a(n-3)+a(n-6), seq(a(i)=[14, 24, 41, 70, 120, 207][i-3], i=4..9)}, a(n), remember):

%p map(f, [$0..35]); # _Robert Israel_, Sep 19 2017

%t LinearRecurrence[{2,0,-1,0,0,1}, {1, 2, 4, 8, 14, 24}, 50] (* _G. C. Greubel_, Sep 19 2017 *)

%o (PARI) Vec((1 + x^3)/(1 - 2*x + x^3 - x^6) + 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