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A138147 Concatenation of n digits 1 and n digits 0. 8
10, 1100, 111000, 11110000, 1111100000, 111111000000, 11111110000000, 1111111100000000, 111111111000000000, 11111111110000000000, 1111111111100000000000, 111111111111000000000000, 11111111111110000000000000, 1111111111111100000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Also, a(n) = binary representation of A020522(n), for n>0 (see example).
REFERENCES
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
LINKS
FORMULA
a(n) = (10^(2n) - 10^n)/9 = A002275(n)*10^n. - Omar E. Pol, Apr 16 2008
a(n) = A109241(n-1)*10. - Omar E. Pol, Nov 08 2008
From Colin Barker, Sep 16 2013: (Start)
a(n) = 110*a(n-1) - 1000*a(n-2).
G.f.: 10*x / ((10*x-1)*(100*x-1)). (End)
EXAMPLE
n ... A020522(n) ..... a(n)
1 ....... 2 ........... 10
2 ...... 12 .......... 1100
3 ...... 56 ......... 111000
4 ..... 240 ........ 11110000
5 ..... 992 ....... 1111100000
6 .... 4032 ...... 111111000000
7 ... 16256 ..... 11111110000000
MATHEMATICA
Table[FromDigits[Join[PadRight[{}, n, 1], PadRight[{}, n, 0]]], {n, 15}] (* Harvey P. Dale, Nov 20 2011 *)
PROG
(Magma) [(10^(2*n) - 10^n)/9: n in [1..30]]; // Vincenzo Librandi, Apr 26 2011
(PARI) Vec(10*x/((10*x-1)*(100*x-1)) + O(x^100)) \\ Colin Barker, Sep 16 2013
CROSSREFS
Cf. A002275.
Sequence in context: A290155 A265849 A122230 * A204577 A210995 A325910
KEYWORD
easy,nonn,base
AUTHOR
Omar E. Pol, Mar 29 2008
STATUS
approved

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Last modified March 19 06:05 EDT 2024. Contains 370952 sequences. (Running on oeis4.)