

A078427


Sum of all the decimal digits of numbers from 1 to 10^n.


3



46, 901, 13501, 180001, 2250001, 27000001, 315000001, 3600000001, 40500000001, 450000000001, 4950000000001, 54000000000001, 585000000000001, 6300000000000001, 67500000000000001, 720000000000000001, 7650000000000000001, 81000000000000000001
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OFFSET

1,1


REFERENCES

E. J. Barbeau et al., Five Hundred Mathematical Challenges, Problem 284. pp. 25; 142143, MAA Washington DC, 1995.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (21,120,100).


FORMULA

a(n) = (45*n)*10^(n1)+1.
a(n) = 45*A053541(n)+1.  Lekraj Beedassy, Sep 16 2006
a(n) = 21*a(n1)120*a(n2)+100*a(n3).  Colin Barker, May 23 2014
G.f.: x*(100*x^265*x+46) / ((x1)*(10*x1)^2).  Colin Barker, May 23 2014


EXAMPLE

a(2)=901 because sum of all the digits of numbers from 1 to 10^2 is 901.


MATHEMATICA

LinearRecurrence[{21, 120, 100}, {46, 901, 13501}, 20] (* Harvey P. Dale, Nov 24 2016 *)


PROG

(Magma) [(45*n)*10^(n1)+1: n in [1..30]]; // Vincenzo Librandi, Jun 06 2011
(PARI) Vec(x*(100*x^265*x+46)/((x1)*(10*x1)^2) + O(x^100)) \\ Colin Barker, May 23 2014


CROSSREFS

Cf. A053541, A072290.
Sequence in context: A113922 A160067 A156842 * A002138 A205495 A281655
Adjacent sequences: A078424 A078425 A078426 * A078428 A078429 A078430


KEYWORD

nonn,base,easy


AUTHOR

Shyam Sunder Gupta, Dec 29 2002


EXTENSIONS

Edited by Charles R Greathouse IV, Aug 02 2010
More terms from Colin Barker, May 23 2014


STATUS

approved



