A014925 Number of zeros in numbers 1 to 111...1 (n+1 digits).

1, 21, 321, 4321, 54321, 654321, 7654321, 87654321, 987654321, 10987654321, 120987654321, 1320987654321, 14320987654321, 154320987654321, 1654320987654321, 17654320987654321, 187654320987654321

Offset

1,2

Links

Table of n, a(n) for n=1..17.

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

Formula

a(1) = 1; for n>1, a(n) = n*10^(n-1)+a(n-1).

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

a(n) = 10^n*(n+1)/9-1/81*10^(n+1)+1/81.

a(n) = (10^n*(9*n-1)+1)/81. - Kenneth E. Caviness, Mar 30 2011

E.g.f.: (1 - exp(9*x) + 90*x*exp(9*x))*exp(x)/81. - Ilya Gutkovskiy, May 02 2016

a(n) = Sum_{i=0..n}(i*10^(i-1)). - José de Jesús Camacho Medina, Dec 14 2016

Prog

(Magma) [(10^n*(9*n-1)+1)/81: n in [1..25]]; // Vincenzo Librandi, Mar 31 2011
(PARI) a(n) = sum(i=0, n, i*10^(i-1)); \\ Michel Marcus, Dec 15 2016

Crossrefs

Cf. A033713.

Sequence in context: A057138 A104759 A138793 * A000422 A060554 A057610

Adjacent sequences: A014922 A014923 A014924 * A014926 A014927 A014928

Keyword

nonn,easy,base

Author

Olivier Gérard

Extensions

Better description from Stephen G Penrice, Oct 03 2000

Status

approved