cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A078427 Sum of all the decimal digits of numbers from 1 to 10^n.

Original entry on oeis.org

46, 901, 13501, 180001, 2250001, 27000001, 315000001, 3600000001, 40500000001, 450000000001, 4950000000001, 54000000000001, 585000000000001, 6300000000000001, 67500000000000001, 720000000000000001, 7650000000000000001, 81000000000000000001
Offset: 1

Views

Author

Shyam Sunder Gupta, Dec 29 2002

Keywords

Examples

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

References

  • E. J. Barbeau et al., Five Hundred Mathematical Challenges, Problem 284. pp. 25; 142-143, MAA Washington DC, 1995.

Crossrefs

Programs

  • Magma
    [(45*n)*10^(n-1)+1: n in [1..30]]; // Vincenzo Librandi, Jun 06 2011
    
  • Mathematica
    LinearRecurrence[{21,-120,100},{46,901,13501},20] (* Harvey P. Dale, Nov 24 2016 *)
  • PARI
    Vec(-x*(100*x^2-65*x+46)/((x-1)*(10*x-1)^2) + O(x^100)) \\ Colin Barker, May 23 2014

Formula

a(n) = (45*n)*10^(n-1)+1.
a(n) = 45*A053541(n)+1. - Lekraj Beedassy, Sep 16 2006
a(n) = 21*a(n-1)-120*a(n-2)+100*a(n-3). - Colin Barker, May 23 2014
G.f.: -x*(100*x^2-65*x+46) / ((x-1)*(10*x-1)^2). - Colin Barker, May 23 2014

Extensions

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