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.

A168278 (10*n + 5*(-1)^n + 3)/4.

Original entry on oeis.org

2, 7, 7, 12, 12, 17, 17, 22, 22, 27, 27, 32, 32, 37, 37, 42, 42, 47, 47, 52, 52, 57, 57, 62, 62, 67, 67, 72, 72, 77, 77, 82, 82, 87, 87, 92, 92, 97, 97, 102, 102, 107, 107, 112, 112, 117, 117, 122, 122, 127, 127, 132, 132, 137, 137, 142, 142, 147, 147, 152, 152, 157
Offset: 1

Views

Author

Vincenzo Librandi, Nov 22 2009

Keywords

Links

Crossrefs

Cf. A016873, A168282.

Programs

  • Magma
    [5*n/2+3/4+5*(-1)^n/4: n in [1..70]]; // Vincenzo Librandi, Sep 16 2013
  • Mathematica
    Table[5 n/2 + 3/4 + 5 (-1)^n/4, {n, 70}] (* Bruno Berselli, Sep 16 2013 *)
CoefficientList[Series[- (- 2 - 5 x + 2 x^2) / ((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 16 2013 *)

Formula

G.f.: x*(2 + 5*x - 2*x^2)/( (1+x)*(x-1)^2 ). - R. J. Mathar, Jan 05 2011
a(n) = A016873(floor(n/2)). - R. J. Mathar, Jan 05 2011
a(n) = A168282(n) + 1. - Bruno Berselli, Sep 16 2013
E.g.f.: (1/4)*(5 - 8*exp(x) + (3 + 10*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 16 2016

Extensions

New definition by R. J. Mathar, Jan 05 2011

A168457 a(n) = (10*n + 5*(-1)^n - 1)/2.

Original entry on oeis.org

2, 12, 12, 22, 22, 32, 32, 42, 42, 52, 52, 62, 62, 72, 72, 82, 82, 92, 92, 102, 102, 112, 112, 122, 122, 132, 132, 142, 142, 152, 152, 162, 162, 172, 172, 182, 182, 192, 192, 202, 202, 212, 212, 222, 222, 232, 232, 242, 242, 252, 252, 262, 262, 272, 272, 282
Offset: 1

Views

Author

Vincenzo Librandi, Nov 26 2009

Keywords

Links

Crossrefs

Cf. A017293, A168459, A168282.

Programs

  • Magma
    [2+10*Floor(n/2): n in [1..70]]; // Vincenzo Librandi, Sep 19 2013
  • Mathematica
    Table[5 n + 5 (-1)^n/2 - 1/2, {n, 60}] (* Bruno Berselli, Sep 16 2013 *)
Table[2 + 10 Floor[n/2], {n, 70}] (* or *) CoefficientList[Series[2 (1 + 5 x - x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 19 2013 *)
LinearRecurrence[{1,1,-1},{2,12,12},80] (* Harvey P. Dale, Dec 27 2024 *)

Formula

a(n) = 10*n - a(n-1) - 6 for n>1, a(1)=2.
From Bruno Berselli, Sep 16 2013: (Start)
G.f.: 2*x*(1 + 5*x - x^2)/((1+x)*(1-x)^2).
a(n) = A168459(n) + 1 = 2*A168282(n).
a(n) = a(n-1) +a(n-2) -a(n-3). (End)
a(n) = 2 + 10*Floor(n/2). - Vincenzo Librandi, Sep 19 2013
E.g.f.: (1/2)*(5 - 4*exp(x) + (10*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 22 2016

Extensions

New definition by Bruno Berselli, Sep 16 2013

A168459 a(n) = (10*n + 5*(-1)^n - 3)/2.

Original entry on oeis.org

1, 11, 11, 21, 21, 31, 31, 41, 41, 51, 51, 61, 61, 71, 71, 81, 81, 91, 91, 101, 101, 111, 111, 121, 121, 131, 131, 141, 141, 151, 151, 161, 161, 171, 171, 181, 181, 191, 191, 201, 201, 211, 211, 221, 221, 231, 231, 241, 241, 251, 251, 261, 261, 271, 271, 281
Offset: 1

Views

Author

Vincenzo Librandi, Nov 26 2009

Keywords

Links

Crossrefs

Cf. A017281, A168457, A168282.

Programs

  • Magma
    [1+10*Floor(n/2): n in [1..70]]; // Vincenzo Librandi, Sep 19 2013
  • Mathematica
    Table[5 n + 5 (-1)^n/2 - 3/2, {n, 60}] (* Bruno Berselli, Sep 16 2013 *)
Table[1 + 10 Floor[n/2], {n, 70}] (* or *) CoefficientList[Series[(1 + 10 x - x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 19 2013 *)

Formula

a(n) = 10*n - a(n-1) - 8 with n>1, a(1)=1.
From Bruno Berselli, Sep 16 2013: (Start)
G.f.: x*(1 + 10*x - x^2)/((1+x)*(1-x)^2).
a(n) = A168457(n) - 1 = 2*A168282(n) - 1.
a(n) = a(n-1) +a(n-2) -a(n-3). (End)
a(n) = 1 + 10*floor(n/2). - Vincenzo Librandi, Sep 19 2013
E.g.f.: (1/2)*(5 - 2*exp(x) + (10*x - 3)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 23 2016

Extensions

New definition by Bruno Berselli, Sep 16 2013
Showing 1-3 of 3 results.

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