A098611 a(n) = 10^n - (-1)^n.

0, 11, 99, 1001, 9999, 100001, 999999, 10000001, 99999999, 1000000001, 9999999999, 100000000001, 999999999999, 10000000000001, 99999999999999, 1000000000000001, 9999999999999999, 100000000000000001, 999999999999999999, 10000000000000000001

Offset: 0

Author

Henry Bottomley, Sep 17 2004

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (9,10).

Crossrefs

Cf. A015585, A098609, A098610.

Programs

Magma

[10^n-(-1)^n : n in [0..30]]; // Wesley Ivan Hurt, Apr 05 2015

Maple

A098611:=n->10^n-(-1)^n: seq(A098611(n), n=0..30); # Wesley Ivan Hurt, Apr 05 2015

Mathematica

Table[(10^n - (-1)^n), {n, 0, 30}] (* or *)
CoefficientList[Series[11 x/(1 - 9 x - 10 x^2), {x, 0, 30}], x] (* Wesley Ivan Hurt, Apr 05 2015 *)
LinearRecurrence[{9, 10}, {0, 11}, 20] (* Vincenzo Librandi, Apr 06 2015 *)

PARI

vector(20,n, 10^(n-1)+(-1)^n) \\ Derek Orr, Apr 05 2015

Formula

a(n) = A098610(n) - 2*(-1)^n = A098609(n)/A098610(n).

From Wesley Ivan Hurt, Apr 05 2015: (Start)

G.f.: 11*x/(1-9*x-10*x^2).

a(n) = 9*a(n-1) + 10*a(n-2). (End)

From Elmo R. Oliveira, Aug 17 2024: (Start)

E.g.f.: exp(-x)*(exp(11*x) - 1).

a(n) = 11*A015585(n). (End)