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.

A016225 Expansion of 1/((1-x)(1-4x)(1-10x)).

Original entry on oeis.org

1, 15, 171, 1795, 18291, 184275, 1848211, 18503955, 185126931, 1851618835, 18517586451, 185181456915, 1851836938771, 18518458866195, 185184946575891, 1851850897414675, 18518514700769811, 185185169914190355
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A080249, A080250, A002450.

Programs

Formula

G.f.: 1/((1-x)*(1-4*x)*(1-10*x)).
a(n) = (50*10^n-24*4^n+1)/27. - Paul Barry, Feb 17 2003
a(n) = 14*a(n-1)-40*a(n-2)+1, n>=2. - Vincenzo Librandi, Feb 10 2011
a(n) = 15*a(n-1) - 54*a(n-2) + 40*a(n-3). - Wesley Ivan Hurt, May 25 2024

A080250 Expansion of 1/((1-x)(1-4x)(1-10x)(1-20x)).

Original entry on oeis.org

1, 35, 871, 19215, 402591, 8236095, 166570111, 3349906175, 67183250431, 1345516627455, 26928850135551, 538762184167935, 10777095520297471, 215560428864815615, 4311393762242888191, 86229727095755178495
Offset: 0

Views

Author

Paul Barry, Feb 17 2003

Keywords

Comments

Column k=3 in number triangle A080249.

Links

Crossrefs

Cf. A080249, A016225, A000292.

Programs

  • Magma
    [(1350*20^n-950*10^n+114*4^n-1)/513: n in [0..20]]; // Vincenzo Librandi, Aug 05 2013
  • Mathematica
    CoefficientList[Series[1/((1-x)(1-4x)(1-10x)(1-20x)),{x,0,20}],x] (* or *) Table[(1350*20^n-950*10^n+114*4^n-1)/513,{n,0,20}] (* or *) LinearRecurrence[{35,-354,1120,-800},{1,35,871,19215},21] (* Harvey P. Dale, Apr 25 2011 *)

Formula

G.f.: 1/((1-x)*(1-4*x)*(1-10*x)*(1-20*x)).
a(n) = (1350*20^n-950*10^n+114*4^n-1)/513.
a(0)=1, a(1)=35, a(2)=871, a(3)=19215, a(n) = 35*a(n-1) -354*a(n-2) +1120*a(n-3) -800*a(n-4). - Harvey P. Dale, Apr 25 2011

Extensions

Corrected by T. D. Noe, Nov 08 2006

A227273 Expansion of 1/((1-x)*(1-4*x)*(1-10*x)*(1-20*x)*(1-35*x)).

Original entry on oeis.org

1, 70, 3321, 135450, 5143341, 188253030, 6755426161, 239789821810, 8459827013781, 297439462109790, 10437310023978201, 365844613023404970, 12815338551339471421, 448752409725746315350, 15710645734163363925441, 549958830422813492568930, 19250283677858902044252261
Offset: 0

Views

Author

Yahia Kahloune, Jul 04 2013

Keywords

Comments

Note that the denominator has 5 tetrahedral numbers: 1, 4, 10, 20, 35.

Links

Crossrefs

Column k=4 of A080249.
Cf. A080250, A002450, A000292.

Programs

  • Mathematica
    CoefficientList[Series[1/((1 - x) (1 - 4 x) (1 - 10 x) (1 - 20 x) (1 - 35 x)), {x, 0, 50}], x] (* G. C. Greubel, Oct 02 2017 *)
  • PARI
    Vec(1/((1-x)*(1-4*x)*(1-10*x)*(1-20*x)*(1-35*x)) + O(x^50)) \\ Michel Marcus, May 23 2014

Formula

a(n) = (2736*35^(n+4) - 23715*20^(n+4) + 80104*10^(n+4) - 121125*4^(n+4) + 62000)/1081404000.

Extensions

Typo in a(7) fixed by Colin Barker, May 23 2014
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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