A103456 a(n) = 0^n + 10^n - 1.

1, 9, 99, 999, 9999, 99999, 999999, 9999999, 99999999, 999999999, 9999999999, 99999999999, 999999999999, 9999999999999, 99999999999999, 999999999999999, 9999999999999999, 99999999999999999, 999999999999999999

Offset: 0

Author

Paul Barry, Feb 06 2005

Keywords

• easy
• nonn

Comments

A transform of 10^n under the matrix A103452.

Except for n = 0, the same as A002283. - Felix Fröhlich, Jun 22 2021

Links

• G. C. Greubel, Table of n, a(n) for n = 0..450
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A002283, A103452.

Programs

Magma

[1] cat [10^n -1: n in [1..40]]; // G. C. Greubel, Jun 21 2021

Mathematica

Table[Boole[n==0] + 10^n -1, {n,0,40}] (* Alonso del Arte, Nov 03 2019 *)

PARI

a(n) = 0^n + 10^n - 1 \\ Felix Fröhlich, Jun 22 2021

PARI

Vec((1 - 2*x + 10*x^2)/((1 - x)*(1 - 10*x)) + O(x^20)) \\ Felix Fröhlich, Jun 22 2021

Sage

[1]+[10^n -1 for n in (1..40)] # G. C. Greubel, Jun 21 2021

Formula

G.f.: (1 - 2*x + 10*x^2)/((1 - x)*(1 - 10*x));

a(n) = Sum_{k = 0..n} A103452(n, k)*10^k;

a(n) = Sum_{k = 0..n} (2*0^(n-k) - 1)*0^(k*(n-k))*10^k.

a(n) = A002283(n), n > 0. - R. J. Mathar, Aug 30 2008

E.g.f.: 1 - exp(x) + exp(10*x). - G. C. Greubel, Jun 21 2021