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%I #25 Sep 08 2022 08:45:33
%S 10,1100,111000,11110000,1111100000,111111000000,11111110000000,
%T 1111111100000000,111111111000000000,11111111110000000000,
%U 1111111111100000000000,111111111111000000000000,11111111111110000000000000,1111111111111100000000000000
%N Concatenation of n digits 1 and n digits 0.
%C Also, a(n) = binary representation of A020522(n), for n>0 (see example).
%D 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 Vincenzo Librandi, <a href="/A138147/b138147.txt">Table of n, a(n) for n = 1..95</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (110,-1000).
%F a(n) = (10^(2n) - 10^n)/9 = A002275(n)*10^n. - _Omar E. Pol_, Apr 16 2008
%F a(n) = A109241(n-1)*10. - _Omar E. Pol_, Nov 08 2008
%F From _Colin Barker_, Sep 16 2013: (Start)
%F a(n) = 110*a(n-1) - 1000*a(n-2).
%F G.f.: 10*x / ((10*x-1)*(100*x-1)). (End)
%e n ... A020522(n) ..... a(n)
%e 1 ....... 2 ........... 10
%e 2 ...... 12 .......... 1100
%e 3 ...... 56 ......... 111000
%e 4 ..... 240 ........ 11110000
%e 5 ..... 992 ....... 1111100000
%e 6 .... 4032 ...... 111111000000
%e 7 ... 16256 ..... 11111110000000
%t Table[FromDigits[Join[PadRight[{},n,1],PadRight[{},n,0]]],{n,15}] (* _Harvey P. Dale_, Nov 20 2011 *)
%o (Magma) [(10^(2*n) - 10^n)/9: n in [1..30]]; // _Vincenzo Librandi_, Apr 26 2011
%o (PARI) Vec(10*x/((10*x-1)*(100*x-1)) + O(x^100)) \\ _Colin Barker_, Sep 16 2013
%Y Cf. A020522, A138144, A138145, A138720.
%Y Cf. A002275.
%Y Cf. A109241, A138118, A138119, A138120, A138146, A138721, A138826. - _Omar E. Pol_, Nov 08 2008
%K easy,nonn,base
%O 1,1
%A _Omar E. Pol_, Mar 29 2008
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