A098609 a(n) = 100^n - 1.

0, 99, 9999, 999999, 99999999, 9999999999, 999999999999, 99999999999999, 9999999999999999, 999999999999999999, 99999999999999999999, 9999999999999999999999, 999999999999999999999999, 99999999999999999999999999, 9999999999999999999999999999, 999999999999999999999999999999

Offset: 0

Author

Henry Bottomley, Sep 17 2004

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• Index entries for linear recurrences with constant coefficients, signature (101,-100).

Crossrefs

Cf. A002283, A062397, A098608.

Programs

Magma

[100^n-1: n in [0..20]]; // Vincenzo Librandi, Sep 23 2016

Mathematica

Table[100^n - 1, {n, 0, 20}] (* Vincenzo Librandi, Sep 23 2016 *)

Formula

a(n) = 100*a(n-1) + 99 = A002283(2*n) = A098608(n) - 1.

From Chai Wah Wu, Sep 22 2016: (Start)

a(n) = 101*a(n-1) - 100*a(n-2) for n > 1.

G.f.: 99*x/((x - 1)*(100*x - 1)). (End)

E.g.f.: exp(x)*(exp(99*x) - 1). - Stefano Spezia, Aug 05 2024

a(n) = A002283(n)*A062397(n). - Elmo R. Oliveira, Sep 09 2024