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.

Showing 1-2 of 2 results.

A168333 a(n) = (14*n + 7*(-1)^n + 1)/4.

Original entry on oeis.org

2, 9, 9, 16, 16, 23, 23, 30, 30, 37, 37, 44, 44, 51, 51, 58, 58, 65, 65, 72, 72, 79, 79, 86, 86, 93, 93, 100, 100, 107, 107, 114, 114, 121, 121, 128, 128, 135, 135, 142, 142, 149, 149, 156, 156, 163, 163, 170, 170, 177, 177, 184, 184, 191, 191, 198, 198, 205, 205
Offset: 1

Views

Author

Vincenzo Librandi, Nov 23 2009

Keywords

Crossrefs

Programs

  • Magma
    [n eq 1 select 2 else 7*n-Self(n-1)-3: n in [1..70]]; // Vincenzo Librandi, Sep 17 2013
  • Mathematica
    CoefficientList[Series[(2 + 7 x - 2 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 17 2013 *)
    LinearRecurrence[{1,1,-1},{2,9,9},70] (* Harvey P. Dale, Mar 13 2014 *)

Formula

a(n) = 7*n - a(n-1) - 3, with n>1, a(1)=2.
G.f.: x*(2 + 7*x - 2*x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 17 2013
a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Sep 17 2013
a(n) = A168331(n) - 1 = A168337(n) + 1 = A168212(n) - 2 = A168374(n) + 2. - Bruno Berselli, Sep 17 2013
E.g.f.: (1/4)*(7 - 8*exp(x) + (14*x + 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 18 2016

Extensions

New definition by Bruno Berselli, Sep 17 2013

A168376 a(n) = (14*n - 7*(-1)^n - 9)/4.

Original entry on oeis.org

3, 3, 10, 10, 17, 17, 24, 24, 31, 31, 38, 38, 45, 45, 52, 52, 59, 59, 66, 66, 73, 73, 80, 80, 87, 87, 94, 94, 101, 101, 108, 108, 115, 115, 122, 122, 129, 129, 136, 136, 143, 143, 150, 150, 157, 157, 164, 164, 171, 171, 178, 178, 185, 185, 192, 192, 199, 199, 206
Offset: 1

Views

Author

Vincenzo Librandi, Nov 24 2009

Keywords

Crossrefs

Cf. A168331.

Programs

  • Magma
    [n eq 1 select 3 else 7*n-Self(n-1)-8: n in [1..70]]; // Vincenzo Librandi, Sep 17 2013
    
  • Mathematica
    Table[7 n/2 - (7 (-1)^n + 9)/4, {n, 60}] (* Bruno Berselli, Sep 17 2013 *)
    CoefficientList[Series[(3 + 4 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 17 2013 *)
  • PARI
    a(n)=(14*n-7*(-1)^n-9)/4 \\ Charles R Greathouse IV, Jul 19 2016

Formula

a(n) = 7*n - a(n-1) - 8, with n>1, a(1)=3.
a(n) = A168331(n-1), n>1. - R. J. Mathar, Nov 25 2009
G.f.: x*(3 + 4*x^2)/((1+x) * (x-1)^2). - R. J. Mathar, Nov 25 2009
a(n) = 3 + 7*floor((n-1)/2). - Bruno Berselli, Sep 18 2013
From G. C. Greubel, Jul 19 2016: (Start)
E.g.f.: (1/4)*(-7 + 16*exp(x) + (14*x - 9)*exp(2*x))*exp(-x).
a(n) = a(n-1) + a(n-2) - a(n-3). (End)

Extensions

Definition rewritten using Mathar's formula by Bruno Berselli, Sep 17 2013
Showing 1-2 of 2 results.