A105694 a(n) = ceiling(10^n - 10^(n-2)).

1, 10, 99, 990, 9900, 99000, 990000, 9900000, 99000000, 990000000, 9900000000, 99000000000, 990000000000, 9900000000000, 99000000000000, 990000000000000, 9900000000000000, 99000000000000000, 990000000000000000, 9900000000000000000, 99000000000000000000, 990000000000000000000

Offset

0,2

Comments

Apply the Riordan array (1-x,x/(1+x)) to 11^n.

Links

Table of n, a(n) for n=0..21.

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

Formula

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

a(n) = 10^n - 10^(n-2), n>1; a(0)=1, a(1)=10.

From Elmo R. Oliveira, Jun 13 2026: (Start)

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

E.g.f.: (1 + 10*x + 99*exp(10*x))/100. (End)

Mathematica

Join[{1, 10}, NestList[10#&, 99, 20]] (* Harvey P. Dale, Sep 18 2022 *)

Crossrefs

Cf. A011557.

Sequence in context: A179556 A179477 A179555 * A179557 A300000 A213454

Adjacent sequences: A105691 A105692 A105693 * A105695 A105696 A105697

Keyword

nonn,easy,changed

Author

Paul Barry, Apr 17 2005

Extensions

More terms from Elmo R. Oliveira, Jun 13 2026

Status

approved