cp's OEIS Frontend

A138721 Concatenation of n digits 1, n digits 0 and n digits 1.

%I A138721 #30 Aug 02 2024 15:55:33
%S A138721 101,110011,111000111,111100001111,111110000011111,111111000000111111,
%T A138721 111111100000001111111,111111110000000011111111,
%U A138721 111111111000000000111111111,111111111100000000001111111111,111111111110000000000011111111111,111111111111000000000000111111111111
%N A138721 Concatenation of n digits 1, n digits 0 and n digits 1.
%C A138721 a(n) is also A145641(n) written in base 2. - _Omar E. Pol_, Oct 15 2008
%C A138721 a(n) has 3n digits. - _Omar E. Pol_, Nov 12 2008
%H A138721 Paolo Xausa, <a href="/A138721/b138721.txt">Table of n, a(n) for n = 1..300</a>
%H A138721 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1111,-112110,1111000,-1000000).
%F A138721 G.f.: x*(101000*x^2 - 2200*x + 101) / ((x-1)*(10*x-1)*(100*x-1)*(1000*x-1)). - _Colin Barker_, Sep 16 2013
%F A138721 a(n) = (100^n+1)*(10^n-1)/9. - _Paolo Xausa_, Aug 02 2024
%e A138721 From _Omar E. Pol_, Nov 12 2008: (Start)
%e A138721 n         Successive digits of a(n)
%e A138721 1                 ( 1 0 1 )
%e A138721 2              ( 1 1 0 0 1 1 )
%e A138721 3           ( 1 1 1 0 0 0 1 1 1 )
%e A138721 4        ( 1 1 1 1 0 0 0 0 1 1 1 1 )
%e A138721 5     ( 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 )
%e A138721 (End)
%p A138721 a:= n-> parse(cat(1$n,0$n,1$n)):
%p A138721 seq(a(n), n=1..14);  # _Alois P. Heinz_, Mar 03 2022
%t A138721 Table[(100^n + 1)*(10^n - 1)/9, {n, 15}] (* _Paolo Xausa_, Aug 02 2024 *)
%o A138721 (PARI) Vec(x*(101000*x^2-2200*x+101)/((x-1)*(10*x-1)*(100*x-1)*(1000*x-1)) + O(x^100)) \\ _Colin Barker_, Sep 16 2013
%Y A138721 Cf. A000533, A135577, A138120, A138144, A138145, A138146, A138826, A145641, A147757, A147759.
%K A138721 nonn,base,easy
%O A138721 1,1
%A A138721 _Omar E. Pol_, Mar 29 2008