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.

A087539 First differences of A011849.

Original entry on oeis.org

0, 0, 1, 2, 3, 5, 7, 10, 12, 15, 18, 22, 26, 30, 35, 40, 46, 51, 57, 63, 70, 77, 84, 92, 100, 109, 117, 126, 135, 145, 155, 165, 176, 187, 199, 210, 222, 234, 247, 260, 273, 287, 301, 316, 330, 345, 360, 376, 392, 408, 425, 442, 460, 477, 495, 513
Offset: 1

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Author

Ralf Stephan, Oct 24 2003

Keywords

Formula

[ C(n+1, 3)/3 ] - [ C(n, 3)/3 ].
G.f.: [x^3(1-x+x^2)(1-x^2+x^3)]/[(1-x)^3(1+x^3+x^6)].

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

A011857 Triangle of numbers [ C(n,k)/k ], k=1..n-1.

Original entry on oeis.org

2, 3, 1, 4, 3, 1, 5, 5, 3, 1, 6, 7, 6, 3, 1, 7, 10, 11, 8, 4, 1, 8, 14, 18, 17, 11, 4, 1, 9, 18, 28, 31, 25, 14, 5, 1, 10, 22, 40, 52, 50, 35, 17, 5, 1, 11, 27, 55, 82, 92, 77, 47, 20, 6, 1, 12, 33, 73, 123, 158, 154, 113, 61, 24, 6, 1, 13, 39, 95, 178, 257, 286, 245, 160
Offset: 2

Views

Author

N. J. A. Sloane

Keywords

Crossrefs

Columns include A011848, A011849, A011850, A011851, A011852, A011853, A011854, A011855, A011856. Row sums are in A101687. Cf. A011847.

Programs

  • Mathematica
    Flatten[Table[Floor[Binomial[n,k]/k],{n,20},{k,n-1}]] (* Harvey P. Dale, Apr 19 2015 *)
Showing 1-3 of 3 results.

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

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