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.

A055610 A companion sequence to A011896.

Original entry on oeis.org

0, 0, 0, 1, 2, 5, 9, 15, 24, 36, 52, 71, 95, 123, 156, 195, 240, 292, 350, 416, 489, 570, 660, 759, 868, 986, 1115, 1254, 1404, 1566, 1740, 1927, 2126, 2339, 2565, 2805, 3060, 3330, 3616, 3917, 4235, 4569, 4920, 5289, 5676, 6082, 6506, 6950, 7413, 7896
Offset: 0

Views

Author

Michael Somos, Jun 02 2000

Keywords

Examples

			x^3 + 2*x^4 + 5*x^5 + 9*x^6 + 15*x^7 + 24*x^8 + 36*x^9 + 52*x^10 + ...

Links

Crossrefs

Cf. A011896.

Programs

  • PARI
    a(n) = ceil( n * (n-1) * (n-2) / 14)

Formula

G.f.: x^3 * (1 - x + 2*x^2 - x^3 + x^4 + x^5) / ((1 - x)^3 * (1 - x^7)).
a(n) = -A011896(2 - n).

A011886 a(n) = floor(n*(n-1)*(n-2)/4).

Original entry on oeis.org

0, 0, 0, 1, 6, 15, 30, 52, 84, 126, 180, 247, 330, 429, 546, 682, 840, 1020, 1224, 1453, 1710, 1995, 2310, 2656, 3036, 3450, 3900, 4387, 4914, 5481, 6090, 6742, 7440, 8184, 8976, 9817, 10710, 11655, 12654, 13708, 14820, 15990, 17220, 18511, 19866, 21285
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Sequences of the form floor(n*(n-1)*(n-2)/m): A007531 (m=1), A135503 (m=2), A007290 (m=3), this sequence (m=4), A011887 (m=5), A000292 (m=6), A011889 (m=7), A011890 (m=8), A011891 (m=9), A011892 (m=10), A011893 (m=11), A011894 (m=12), A011895 (m=13), A011896 (m=14), A011897 (m=15), A011898 (m=16), A011899 (m=17), A011849 (m=18), A011901 (m=19), A011902 (m=20), A011903 (m=21), A011904 (m=22), A011905 (m=23), A011842 (m=24), A011907 (m=25), A011908 (m=26), A011909 (m=27), A011910 (m=28), A011911 (m=29), A011912 (m=30), A011912 (m=31), A011913 (m=32).

Programs

  • Magma
    [Floor(n*(n-1)*(n-2)/4): n in [0..50]]; // Vincenzo Librandi, Jul 07 2012
  • Mathematica
    Table[Floor[(n(n-1)(n-2))/4],{n,0,50}] (* or *) LinearRecurrence[{3,-3,1,1, -3,3,-1},{0,0,0,1,6,15,30}, 50] (* Harvey P. Dale, Feb 25 2012 *)
CoefficientList[Series[x^3*(1+3*x+2*x^3)/((1-x)^3*(1-x^4)),{x,0,50}],x] (* Vincenzo Librandi, Jul 07 2012 *)
  • SageMath
    [3*binomial(n,3)//2 for n in range(51)] # G. C. Greubel, Oct 06 2024

Formula

From R. J. Mathar, Apr 15 2010: (Start)
a(n) = +3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7).
G.f.: x^3*(1+3*x+2*x^3) / ( (1-x)^4*(1+x)*(1+x^2) ). (End)
a(n) = floor(Sum_{k=0..n} n*(k+1)/2) for n >= -2. - William A. Tedeschi, Sep 10 2010

Extensions

More terms from William A. Tedeschi, Sep 10 2010
Showing 1-2 of 2 results.

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

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