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A103456 a(n) = 0^n + 10^n - 1. 1
1, 9, 99, 999, 9999, 99999, 999999, 9999999, 99999999, 999999999, 9999999999, 99999999999, 999999999999, 9999999999999, 99999999999999, 999999999999999, 9999999999999999, 99999999999999999, 999999999999999999 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A transform of 10^n under the matrix A103452.

LINKS

Table of n, a(n) for n=0..18.

FORMULA

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

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

a(n) = 10*a(n-1) + 9 - 10*(binomial(2*(n-1), n-1) mod 2), with a(0) = 1 - Paolo P. Lava, Jun 04 2009

MATHEMATICA

Table[Boole[n == 0] + 10^n - 1, {n, 0, 39}] (* Alonso del Arte, Nov 03 2019 *)

CROSSREFS

Sequence in context: A242809 A108908 A116260 * A002283 A155157 A264005

Adjacent sequences:  A103453 A103454 A103455 * A103457 A103458 A103459

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Feb 06 2005

STATUS

approved

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Last modified September 20 20:02 EDT 2020. Contains 337265 sequences. (Running on oeis4.)