A138147 Concatenation of n digits 1 and n digits 0.

10, 1100, 111000, 11110000, 1111100000, 111111000000, 11111110000000, 1111111100000000, 111111111000000000, 11111111110000000000, 1111111111100000000000, 111111111111000000000000, 11111111111110000000000000, 1111111111111100000000000000, 111111111111111000000000000000

Offset: 1

Author

Omar E. Pol, Mar 29 2008

Keywords

• easy
• nonn
• base

Comments

Also, a(n) = binary representation of A020522(n), for n>0 (see example).

Examples

			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
		

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

• Vincenzo Librandi, Table of n, a(n) for n = 1..95
• Index entries for linear recurrences with constant coefficients, signature (110,-1000).

Crossrefs

Cf. A002275, A020522, A138144, A138145, A138720, A276352.

Cf. A109241, A138118, A138119, A138120, A138146, A138721, A138826. - Omar E. Pol, Nov 08 2008

Programs

Magma

[(10^(2*n) - 10^n)/9: n in [1..30]]; // Vincenzo Librandi, Apr 26 2011

Mathematica

Table[FromDigits[Join[PadRight[{},n,1],PadRight[{},n,0]]],{n,15}] (* Harvey P. Dale, Nov 20 2011 *)

PARI

Vec(10*x/((10*x-1)*(100*x-1)) + O(x^100)) \\ Colin Barker, Sep 16 2013

Formula

a(n) = (10^(2*n) - 10^n)/9 = A002275(n)*10^n. - Omar E. Pol, Apr 16 2008

a(n) = 10*A109241(n-1). - 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)

From Elmo R. Oliveira, Jun 13 2025: (Start)

E.g.f.: exp(10*x)*(exp(90*x) - 1)/9.

a(n) = A276352(n)/9. (End)