cp's OEIS Frontend

A152775 Numbers with 3n binary digits where every run length is 3, written in binary.

%I A152775 #28 Apr 20 2024 10:27:33
%S A152775 111,111000,111000111,111000111000,111000111000111,111000111000111000,
%T A152775 111000111000111000111,111000111000111000111000,
%U A152775 111000111000111000111000111,111000111000111000111000111000
%N A152775 Numbers with 3n binary digits where every run length is 3, written in binary.
%C A152775 A152776 written in base 2.
%H A152775 Vincenzo Librandi, <a href="/A152775/b152775.txt">Table of n, a(n) for n = 1..100</a>
%H A152775 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1000,1,-1000).
%F A152775 From _Colin Barker_, Apr 20 2014: (Start)
%F A152775 a(n) = (-1001-999*(-1)^n+2^(4+3*n)*125^(1+n))/18018.
%F A152775 a(n) = 1000*a(n-1)+a(n-2)-1000*a(n-3).
%F A152775 G.f.: 111*x / ((x-1)*(x+1)*(1000*x-1)). (End).
%e A152775 n ... a(n) .............. A152776(n)
%e A152775 1 ... 111 ............... 7
%e A152775 2 ... 111000 ............ 56
%e A152775 3 ... 111000111 ......... 455
%e A152775 4 ... 111000111000 ...... 3640
%e A152775 5 ... 111000111000111 ... 29127
%t A152775 FromDigits/@Table[Flatten[PadRight[{},n,{a,b}]/.{a->{1,1,1},b->{0,0,0}}],{n,10}] (* _Harvey P. Dale_, Mar 23 2012 *)
%t A152775 CoefficientList[Series[111/((x - 1) (x + 1) (1000 x - 1)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Apr 21 2014 *)
%o A152775 (PARI) Vec(111*x / ((x-1)*(x+1)*(1000*x-1)) + O(x^100)) \\ _Colin Barker_, Apr 20 2014
%Y A152775 Cf. A043291, A153435, A152776.
%K A152775 easy,nonn,base
%O A152775 1,1
%A A152775 _Omar E. Pol_, Jan 18 2009