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A138147
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Concatenation of n digits 1 and n digits 0.
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8
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10, 1100, 111000, 11110000, 1111100000, 111111000000, 11111110000000, 1111111100000000, 111111111000000000, 11111111110000000000, 1111111111100000000000, 111111111111000000000000, 11111111111110000000000000, 1111111111111100000000000000
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OFFSET
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1,1
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COMMENTS
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Also, a(n) = binary representation of A020522(n), for n>0 (see example).
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REFERENCES
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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
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LINKS
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FORMULA
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a(n) = 110*a(n-1) - 1000*a(n-2).
G.f.: 10*x / ((10*x-1)*(100*x-1)). (End)
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EXAMPLE
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1 ....... 2 ........... 10
2 ...... 12 .......... 1100
3 ...... 56 ......... 111000
4 ..... 240 ........ 11110000
5 ..... 992 ....... 1111100000
6 .... 4032 ...... 111111000000
7 ... 16256 ..... 11111110000000
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MATHEMATICA
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Table[FromDigits[Join[PadRight[{}, n, 1], PadRight[{}, n, 0]]], {n, 15}] (* Harvey P. Dale, Nov 20 2011 *)
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PROG
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(PARI) Vec(10*x/((10*x-1)*(100*x-1)) + O(x^100)) \\ Colin Barker, Sep 16 2013
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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STATUS
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approved
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