A078761 Sum of the digits of all n-digit numbers.

45, 855, 12600, 166500, 2070000, 24750000, 288000000, 3285000000, 36900000000, 409500000000, 4500000000000, 49050000000000, 531000000000000, 5715000000000000, 61200000000000000, 652500000000000000, 6930000000000000000, 73350000000000000000

Offset

1,1

Links

Table of n, a(n) for n=1..18.

Index entries for linear recurrences with constant coefficients, signature (20,-100).

Formula

First differences of A034967: a(n) = 45*n*10^(n-1) - 45*(n-1)10^(n-2) = 45*(9*n+1)*10^(n-2) - Alexander Adamchuk, Jan 02 2004

G.f.: 45*x*(1 - x)/(1 - 10*x)^2. - Arkadiusz Wesolowski, Jul 12 2012

Example

The sum of the digits of the two-digit numbers 10, 11, 12, ..., 99 is 855. Therefore a(2) = 855.

Mathematica

f[n_] := Module[{i, s}, s = 0; For[i = 10^(n - 1), i < 10^n, i++, s = s + Apply[Plus, IntegerDigits[i]]]; s]; t = Table[f[n], {n, 1, 6}]
n=Range[15] a=45*(9*n+1)*10^(n-2) (Adamchuk)
Rest[CoefficientList[Series[45x (1-x)/(1-10x)^2, {x, 0, 20}], x]] (* Harvey P. Dale, Aug 26 2019 *)

Crossrefs

Cf. A034967.

Sequence in context: A134290 A359933 A341573 * A034967 A199352 A195466

Adjacent sequences: A078758 A078759 A078760 * A078762 A078763 A078764

Keyword

base,nonn

Author

Joseph L. Pe, Jan 08 2003

Status

approved