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

Offset: 0

Author

Lekraj Beedassy, Jun 11 2004

Keywords

• base
• nonn
• easy

Links

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

Crossrefs

Cf. A072290, A078427.

Cf. A011557, A094798.

Programs

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 *)

PARI

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

Formula

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

a(n) = 21*a(n-1)-120*a(n-2)+100*a(n-3). - Colin Barker, May 23 2014

G.f.: -(99*x^2-19*x+1) / ((x-1)*(10*x-1)^2). - Colin Barker, May 23 2014

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

Extensions

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

Further terms from Colin Barker, May 23 2014