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.

A036487 a(n) = floor((n^3)/2).

Original entry on oeis.org

0, 0, 4, 13, 32, 62, 108, 171, 256, 364, 500, 665, 864, 1098, 1372, 1687, 2048, 2456, 2916, 3429, 4000, 4630, 5324, 6083, 6912, 7812, 8788, 9841, 10976, 12194, 13500, 14895, 16384, 17968, 19652, 21437, 23328, 25326, 27436, 29659, 32000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A033430 (bisection), A268201 (bisection).

Programs

  • Maple
    [ seq(floor((n^3)/2), n=0..100) ];
  • Mathematica
    A036487[n_]:=Floor[n^3/2]
Floor[Range[0,40]^3/2] (* or *) LinearRecurrence[{3,-2,-2,3,-1},{0,0,4,13,32},50] (* Harvey P. Dale, Jun 24 2018 *)
  • PARI
    a(n)=n^3\2 \\ Charles R Greathouse IV, Jul 18 2014
  • Sage
    [floor(n^3/2) for n in range(0,41)] # Zerinvary Lajos, Dec 02 2009

Formula

G.f. x^2*(4 + x + x^2)/((1 + x)*(1 - x)^4). - R. J. Mathar, Jan 29 2011
From Stefano Spezia, Sep 09 2022: (Start)
a(n) = ((-1)^n - 1 + 2*n^3)/4.
E.g.f.: (x*(1 + 3*x + x^2)*cosh(x) - (1 - x - 3*x^2 - x^3)*sinh(x))/2. (End)

Extensions

Corrupted b-file corrected by Michael De Vlieger, Jul 18 2014

A271828 a(n) = 4*n^3 - 18*n^2 + 27*n - 12.

Original entry on oeis.org

1, 2, 15, 64, 173, 366, 667, 1100, 1689, 2458, 3431, 4632, 6085, 7814, 9843, 12196, 14897, 17970, 21439, 25328, 29661, 34462, 39755, 45564, 51913, 58826, 66327, 74440, 83189, 92598, 102691, 113492, 125025, 137314, 150383, 164256, 178957, 194510, 210939, 228268, 246521, 265722
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Apr 15 2016

Keywords

Comments

This sequence lists all positive integers n such that 2*n - 3 is a cube. Only for first term 2*n - 3 generates a negative cube that is -1. - Altug Alkan, Apr 15 2016

Links

Crossrefs

Cf. positive integers n such that 2*n + k is a cube: this sequence (k=-3), A050492 (k=-1), A268201 (k=1).

Programs

  • Magma
    [((2*n-1)^3+3)/2: n in [0..40]];
  • Mathematica
    Table[((2 n - 1)^3 + 3)/2, {n, 0, 41}] (* or *)
Rest@ CoefficientList[Series[x (1 - 2 x + 13 x^2 + 12 x^3)/(1 - x)^4, {x, 0, 42}], x] (* Michael De Vlieger, Apr 16 2016 *)
LinearRecurrence[{4,-6,4,-1},{1,2,15,64},70] (* Harvey P. Dale, Jun 06 2022 *)
  • PARI
    lista(nn) = for(n=0, nn, print1(((2*n-1)^3+3)/2, ", ")); \\ Altug Alkan, Apr 15 2016

Formula

a(n+1) = A050492(n)+1.
G.f.: x*(1 - 2*x + 13*x^2 + 12*x^3)/(1 - x)^4. - Ilya Gutkovskiy, Apr 15 2016
Showing 1-2 of 2 results.

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

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