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