A161770 n 1's followed by three 0's.

1000, 11000, 111000, 1111000, 11111000, 111111000, 1111111000, 11111111000, 111111111000, 1111111111000, 11111111111000, 111111111111000, 1111111111111000, 11111111111111000, 111111111111111000, 1111111111111111000, 11111111111111111000, 111111111111111111000

Offset: 1

Author

Jaroslav Krizek, Jun 18 2009

Keywords

• nonn
• easy
• base

Comments

Sequence A159741 written in base 2.

Links

• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A002275, A105279, A124166, A159741.

Programs

Mathematica

Table[FromDigits[PadLeft[{0,0,0},n,1]],{n,4,20}] (* Harvey P. Dale, Aug 07 2023 *)

Formula

a(n) = 1000*(10^n - 1)/9 = 1000*A002275(n).

G.f.: 1000*x/((10*x-1)*(x-1)).

From Elmo R. Oliveira, Jun 18 2025: (Start)

E.g.f.: 1000*exp(x)*(exp(9*x) - 1)/9.

a(n) = 100*A105279(n) = 10*A124166(n).

a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)

Extensions

Edited by Charles R Greathouse IV, Oct 12 2009