A163663 a(0) = 0 and A059153(n-1) written in base 2 otherwise.

0, 100, 11000, 1110000, 111100000, 11111000000, 1111110000000, 111111100000000, 11111111000000000, 1111111110000000000, 111111111100000000000, 11111111111000000000000, 1111111111110000000000000, 111111111111100000000000000, 11111111111111000000000000000

Offset: 0

Author

Jaroslav Krizek, Aug 02 2009

Keywords

• nonn
• base

Comments

The digit pattern of a(n) is: n times 1 and (n+1) times 0.

Links

• Index entries for linear recurrences with constant coefficients, signature (110, -1000).

Programs

Mathematica

Table[FromDigits[Join[PadRight[{},n-1,1],PadRight[{},n,0]]],{n,20}] (* Harvey P. Dale, Aug 29 2015 *)

PARI

x='x+O('x^50); Vec(100*x/((100*x-1)*(10*x-1))) \\ G. C. Greubel, Aug 01 2017

Formula

From R. J. Mathar, Aug 12 2009: (Start)

a(n) = 110*a(n-1) - 1000*a(n-2).

a(n) = 100*A109241(n-1).

G.f.: 100*x/((100*x-1) * (10*x-1)). (End)

From Wesley Ivan Hurt, Jun 22 2013: (Start)

a(n) = (10/9) * (10^n) * (10^n - 1).

a(n) = A002275(n) * 10^(n+1). (End)

E.g.f.: (10/9)*(exp(100*x) - exp(10*x)). - G. C. Greubel, Aug 01 2017

Extensions

Edited by R. J. Mathar, Aug 12 2009