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A138147 Concatenation of n digits 1 and n digits 0. 6

%I

%S 10,1100,111000,11110000,1111100000,111111000000,11111110000000,

%T 1111111100000000,111111111000000000,11111111110000000000,

%U 1111111111100000000000,111111111111000000000000

%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">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. [From _Omar E. Pol_, Nov 08 2008]

%F a(n) = 110*a(n-1)-1000*a(n-2). G.f.: 10*x / ((10*x-1)*(100*x-1)). - _Colin Barker_, Sep 16 2013

%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. [From _Omar E. Pol_, Nov 08 2008]

%K easy,nonn,base

%O 1,1

%A _Omar E. Pol_, Mar 29 2008

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Last modified August 29 05:24 EDT 2015. Contains 261185 sequences.