Voozh

A094797

Number of times 1 is used in writing out all numbers 1 through 10^n.

1, 2, 21, 301, 4001, 50001, 600001, 7000001, 80000001, 900000001, 10000000001, 110000000001, 1200000000001, 13000000000001, 140000000000001, 1500000000000001, 16000000000000001, 170000000000000001, 1800000000000000001, 19000000000000000001

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (21,-120,100).

FORMULA

a(n) = n*10^(n-1) + 1.

From Colin Barker, May 23 2014: (Start)

a(n) = 21*a(n-1) - 120*a(n-2) + 100*a(n-3).

G.f.: -(99*x^2-19*x+1)/((x-1)*(10*x-1)^2). (End)

a(n) = A094798(A011557(n)). - Michel Marcus, Oct 03 2023

From Elmo R. Oliveira, Nov 21 2025: (Start)

E.g.f.: exp(x)*(1 + x*exp(9*x)).

a(n) = A053541(n) + 1 for n > 0. (End)

MATHEMATICA

Table[ n*10^(n - 1) + 1, {n, 0, 17}] (* Robert G. Wilson v, Jun 15 2004 *)

LinearRecurrence[{21, -120, 100}, {1, 2, 21}, 20] (* Harvey P. Dale, Sep 07 2022 *)

PROG

(PARI) Vec(-(99*x^2-19*x+1)/((x-1)*(10*x-1)^2) + O(x^100)) \\ Colin Barker, May 23 2014

CROSSREFS

Cf. A011557, A053541, A072290, A078427, A094798.

Sequence in context: A266969 A229036 A097627 * A359918 A234525 A230382

Adjacent sequences: A094794 A094795 A094796 * A094798 A094799 A094800

KEYWORD

base,nonn,easy

AUTHOR

Lekraj Beedassy, Jun 11 2004

EXTENSIONS

More terms from Robert G. Wilson v, Jun 15 2004

Further terms from Colin Barker, May 23 2014

STATUS

approved

URL: https://oeis.org/A094797

⇱ A094797 - OEIS