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 1-3 of 3 results.

A168332 a(n) = 6 + 7 * floor((n-1)/2).

Original entry on oeis.org

6, 6, 13, 13, 20, 20, 27, 27, 34, 34, 41, 41, 48, 48, 55, 55, 62, 62, 69, 69, 76, 76, 83, 83, 90, 90, 97, 97, 104, 104, 111, 111, 118, 118, 125, 125, 132, 132, 139, 139, 146, 146, 153, 153, 160, 160, 167, 167, 174, 174, 181, 181, 188, 188, 195, 195, 202, 202, 209
Offset: 1

Views

Author

Vincenzo Librandi, Nov 23 2009

Keywords

Crossrefs

Programs

  • Magma
    [n eq 1 select 6 else 7*n-Self(n-1)-2: n in [1..70]]; // Vincenzo Librandi, Sep 17 2013
  • Mathematica
    Table[6 + 7 Floor[(n - 1)/2], {n, 60}] (* Bruno Berselli, Sep 17 2013 *)
    CoefficientList[Series[(6 + x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 17 2013 *)
    LinearRecurrence[{1,1,-1},{6,6,13},60] (* or *) With[{c=NestList[ #+7&,6,30]}, Riffle[c,c]] (* Harvey P. Dale, Aug 29 2015 *)

Formula

a(n) = 7*n - a(n-1) - 2, with n>1, a(1)=6.
G.f.: x*(6 + 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) = (14*n - 7*(-1)^n + 3)/4 = A168374(n+1) - 1 = A168336(n) + 1. - Bruno Berselli, Sep 17 2013
E.g.f.: (1/2)*(2 + (7*x - 2)*cosh(x) + (7*x + 5)*sinh(x)). - G. C. Greubel, Jul 18 2016

Extensions

Definition reformulated by Bruno Berselli at the suggestion of Joerg Arndt and using its formula, Sep 17 2013

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

A168337 a(n) = 1 + 7*floor(n/2).

Original entry on oeis.org

1, 8, 8, 15, 15, 22, 22, 29, 29, 36, 36, 43, 43, 50, 50, 57, 57, 64, 64, 71, 71, 78, 78, 85, 85, 92, 92, 99, 99, 106, 106, 113, 113, 120, 120, 127, 127, 134, 134, 141, 141, 148, 148, 155, 155, 162, 162, 169, 169, 176, 176, 183, 183, 190, 190, 197, 197, 204, 204, 211
Offset: 1

Views

Author

Vincenzo Librandi, Nov 23 2009

Keywords

Crossrefs

Programs

  • Magma
    [7*n/2 + 7*(-1)^n/4 - 3/4: n in [1..70]]; // Vincenzo Librandi, Sep 18 2013
  • Mathematica
    Table[ 1 + 7*floor(n/2) , {n,60}] (* Bruno Berselli, Sep 18 2013 *)
    CoefficientList[Series[(1 + 7 x - x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 18 2013 *)

Formula

a(n) = 7*n - a(n-1) - 5, with n>1, a(1)=1.
From Vincenzo Librandi, Sep 18 2013: (Start)
G.f.: x*(1 + 7*x - x^2)/((1+x)*(x-1)^2).
a(n) = a(n-1) +a(n-2) -a(n-3).
a(n) = (14*n + 7*(-1)^n - 3)/4. (End)
a(n) = A168333(n) - 1 = A168374(n) + 1. - Bruno Berselli, Sep 18 2013
E.g.f.: (1/2)*(-2 + (7*x + 2)*cosh(x) + (7*x - 5)*sinh(x)). - G. C. Greubel, Jul 18 2016

Extensions

New definition by Bruno Berselli, Sep 18 2013
Showing 1-3 of 3 results.