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.

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A093379 Expansion of x(1-2x-2x^2)/((1+x)(1-2x)(1-3x)).

Original entry on oeis.org

0, 1, 2, 5, 12, 31, 82, 225, 632, 1811, 5262, 15445, 45652, 135591, 404042, 1206665, 3609072, 10805371, 32372422, 97029885, 290914892, 872395151, 2616486402, 7848061105, 23541387112, 70618568931, 211844521982, 635511196325
Offset: 0

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Author

Paul Barry, Apr 28 2004

Keywords

Comments

Binomial transform is A085280, with leading zero.

Crossrefs

Cf. A087432.

Programs

  • Mathematica
    CoefficientList[Series[x (1-2x-2x^2)/((1+x)(1-2x)(1-3x)),{x,0,30}],x] (* or *) LinearRecurrence[{4,-1,-6},{0,1,2,5},40] (* Harvey P. Dale, May 10 2019 *)

Formula

a(n)=3^n/12-(-1)^n/12+2^n/3-0^n/3;
a(n)=4a(n-1)-a(n-2)-6a(n-3).
a(n)=A015518(n)/3+A000079(n)/3-0^n/3.
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