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