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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A162814 a(n) = 6*a(n-1)-6*a(n-2) for n > 1; a(0) = 5, a(1) = 18.

Original entry on oeis.org

5, 18, 78, 360, 1692, 7992, 37800, 178848, 846288, 4004640, 18950112, 89672832, 424336320, 2007980928, 9501867648, 44963320320, 212768716032, 1006832374272, 4764381949440, 22545297451008, 106685493009408, 504841173350400
Offset: 0

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Author

Al Hakanson (hawkuu(AT)gmail.com) and Klaus Brockhaus, Jul 14 2009

Keywords

Comments

Binomial transform of A162563. Inverse binomial transform of A162815.

Crossrefs

Programs

  • Magma
    [ n le 2 select 13*n-8 else 6*Self(n-1)-6*Self(n-2): n in [1..22] ];
  • Mathematica
    LinearRecurrence[{6,-6},{5,18},40] (* Harvey P. Dale, Mar 26 2022 *)

Formula

a(n) = ((5+sqrt(3))*(3+sqrt(3))^n+(5-sqrt(3))*(3-sqrt(3))^n)/2.
G.f.: (5-12*x)/(1-6*x+6*x^2).
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