cp's OEIS Frontend

A138147 Concatenation of n digits 1 and n digits 0.

%I A138147 #29 Jun 13 2025 18:16:41
%S A138147 10,1100,111000,11110000,1111100000,111111000000,11111110000000,
%T A138147 1111111100000000,111111111000000000,11111111110000000000,
%U A138147 1111111111100000000000,111111111111000000000000,11111111111110000000000000,1111111111111100000000000000,111111111111111000000000000000
%N A138147 Concatenation of n digits 1 and n digits 0.
%C A138147 Also, a(n) = binary representation of A020522(n), for n>0 (see example).
%D A138147 J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 136, Ex. 4.2.2. - _N. J. A. Sloane_, Jul 27 2012
%H A138147 Vincenzo Librandi, <a href="/A138147/b138147.txt">Table of n, a(n) for n = 1..95</a>
%H A138147 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (110,-1000).
%F A138147 a(n) = (10^(2*n) - 10^n)/9 = A002275(n)*10^n. - _Omar E. Pol_, Apr 16 2008
%F A138147 a(n) = 10*A109241(n-1). - _Omar E. Pol_, Nov 08 2008
%F A138147 From _Colin Barker_, Sep 16 2013: (Start)
%F A138147 a(n) = 110*a(n-1) - 1000*a(n-2).
%F A138147 G.f.: 10*x/((10*x-1)*(100*x-1)). (End)
%F A138147 From _Elmo R. Oliveira_, Jun 13 2025: (Start)
%F A138147 E.g.f.: exp(10*x)*(exp(90*x) - 1)/9.
%F A138147 a(n) = A276352(n)/9. (End)
%e A138147 n ... A020522(n) ..... a(n)
%e A138147 1 ....... 2 ........... 10
%e A138147 2 ...... 12 .......... 1100
%e A138147 3 ...... 56 ......... 111000
%e A138147 4 ..... 240 ........ 11110000
%e A138147 5 ..... 992 ....... 1111100000
%e A138147 6 .... 4032 ...... 111111000000
%e A138147 7 ... 16256 ..... 11111110000000
%t A138147 Table[FromDigits[Join[PadRight[{},n,1],PadRight[{},n,0]]],{n,15}] (* _Harvey P. Dale_, Nov 20 2011 *)
%o A138147 (Magma) [(10^(2*n) - 10^n)/9: n in [1..30]]; // _Vincenzo Librandi_, Apr 26 2011
%o A138147 (PARI) Vec(10*x/((10*x-1)*(100*x-1)) + O(x^100)) \\ _Colin Barker_, Sep 16 2013
%Y A138147 Cf. A002275, A020522, A138144, A138145, A138720, A276352.
%Y A138147 Cf. A109241, A138118, A138119, A138120, A138146, A138721, A138826. - _Omar E. Pol_, Nov 08 2008
%K A138147 easy,nonn,base
%O A138147 1,1
%A A138147 _Omar E. Pol_, Mar 29 2008