cp's OEIS Frontend

A153435 Numbers with 2n binary digits where every run length is 2, written in binary.

%I A153435 #21 Apr 20 2024 10:19:41
%S A153435 11,1100,110011,11001100,1100110011,110011001100,11001100110011,
%T A153435 1100110011001100,110011001100110011,11001100110011001100,
%U A153435 1100110011001100110011,110011001100110011001100
%N A153435 Numbers with 2n binary digits where every run length is 2, written in binary.
%C A153435 A043291 written in base 2.
%H A153435 Vincenzo Librandi, <a href="/A153435/b153435.txt">Table of n, a(n) for n = 1..200</a>
%H A153435 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (100,1,-100).
%F A153435 From _Colin Barker_, Apr 19 2014: (Start)
%F A153435 a(n) = (-101-99*(-1)^n+2^(3+2*n)*25^(1+n))/1818.
%F A153435 a(n) = 100*a(n-1)+a(n-2)-100*a(n-3).
%F A153435 G.f.: 11*x / ((x-1)*(x+1)*(100*x-1)).(End).
%e A153435 n ... a(n) ....... A043291(n)
%e A153435 1 ... 11 ............. 3
%e A153435 2 ... 1100 .......... 12
%e A153435 3 ... 110011 ........ 51
%e A153435 4 ... 11001100 ..... 204
%e A153435 5 ... 1100110011 ... 819
%p A153435 A153435:=n->(-101-99*(-1)^n+2^(3+2*n)*25^(1+n))/1818; seq(A153435(n), n=1..20); # _Wesley Ivan Hurt_, Apr 19 2014
%t A153435 Table[(-101 - 99*(-1)^n + 2^(3 + 2*n)*25^(1 + n))/1818, {n, 20}] (* _Wesley Ivan Hurt_, Apr 19 2014 *)
%t A153435 CoefficientList[Series[11/((x - 1) (x + 1) (100 x - 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Apr 20 2014 *)
%o A153435 (PARI) Vec(11*x / ((x-1)*(x+1)*(100*x-1)) + O(x^100)) \\ _Colin Barker_, Apr 19 2014
%Y A153435 Cf. A043291.
%K A153435 easy,nonn,base
%O A153435 1,1
%A A153435 _Omar E. Pol_, Dec 26 2008