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.

A099914 Expansion of (1+3x)/((1-x)(1-10x)).

Original entry on oeis.org

1, 14, 144, 1444, 14444, 144444, 1444444, 14444444, 144444444, 1444444444, 14444444444, 144444444444, 1444444444444, 14444444444444, 144444444444444, 1444444444444444, 14444444444444444, 144444444444444444, 1444444444444444444, 14444444444444444444, 144444444444444444444
Offset: 0

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Author

Paul Barry, Oct 30 2004

Keywords

Comments

Partial sums of (1+3x)/(1-10x)={1,13,130,1300,...}.

Programs

  • Mathematica
    CoefficientList[Series[(1+3x)/((1-x)(1-10x)),{x,0,20}],x] (* or *) LinearRecurrence[{11,-10},{1,14},20] (* or *) Table[FromDigits[PadRight[{1},n,4]],{n,20}] (* Harvey P. Dale, Mar 05 2023 *)

Formula

a(n) = 10^n*13/9 - 4/9.
a(n) = 11*a(n-1) - 10*a(n-2), a(0)=1, a(1)=14.
E.g.f.: exp(x)*(13*exp(9*x) - 4)/9. - Stefano Spezia, Feb 12 2025