A124166 a(n) = 100*(10^n - 1)/9.

0, 100, 1100, 11100, 111100, 1111100, 11111100, 111111100, 1111111100, 11111111100, 111111111100, 1111111111100, 11111111111100, 111111111111100, 1111111111111100, 11111111111111100, 111111111111111100, 1111111111111111100, 11111111111111111100, 111111111111111111100

Offset

0,2

Links

Table of n, a(n) for n=0..19.

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

Formula

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

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

E.g.f.: 100*exp(x)*(exp(9*x) - 1)/9.

a(n) = 100*A002275(n) = 10*A105279(n).

a(n) = A161770(n)/10 for n >= 1.

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

Maple

a:=n->sum (10^(n-j+2), j=0..n): seq(a(n), n=0..28);

Mathematica

Table[FromDigits[PadLeft[{0, 0}, n, 1]], {n, 2, 20}] (* Harvey P. Dale, Jul 24 2012 *)

Prog

(PARI) concat(0, Vec(100*x/((1-x)*(1-10*x)) + O(x^20))) \\ Elmo R. Oliveira, Jun 18 2025

Crossrefs

Cf. A002275, A105279, A161770.

Sequence in context: A343294 A025421 A300254 * A103175 A163450 A284591

Adjacent sequences: A124163 A124164 A124165 * A124167 A124168 A124169

Keyword

easy,nonn

Author

Zerinvary Lajos, Dec 02 2006

Extensions

More terms from Elmo R. Oliveira, Jun 18 2025

Status

approved