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.

A162816 a(n) = 12*a(n-1)-33*a(n-2) for n > 1; a(0) = 5, a(1) = 33.

Original entry on oeis.org

5, 33, 231, 1683, 12573, 95337, 729135, 5603499, 43180533, 333250929, 2574053559, 19891362051, 153752577165, 1188615978297, 9189556693119, 71050353033627, 549348865530597, 4247524736257473, 32841784272579975, 253933094974463091
Offset: 0

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Author

Klaus Brockhaus, Jul 14 2009

Keywords

Comments

Binomial transform of A143647.

Crossrefs

Cf. A143647.

Programs

  • Magma
    [ n le 2 select 28*n-23 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ];
    
  • Mathematica
    LinearRecurrence[{12,-33},{5,33},40] (* or *) Simplify[With[ {c=Sqrt[3]},Table[(11(5+c)(6+c)^n+(53+7c)(6-c)^n)/(22(6+c)),{n,30}]]] (* Harvey P. Dale, Jun 30 2011 *)
  • PARI
    Vec((5-27*x)/(1-12*x+33*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jun 30 2011

Formula

a(n) = ((5+sqrt(3))*(6+sqrt(3))^n+(5-sqrt(3))*(6-sqrt(3))^n)/2.
G.f.: (5-27*x)/(1-12*x+33*x^2).