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.

A135973 Ceiling(4/3*Pi*n^3).

Original entry on oeis.org

0, 5, 34, 114, 269, 524, 905, 1437, 2145, 3054, 4189, 5576, 7239, 9203, 11495, 14138, 17158, 20580, 24430, 28731, 33511, 38793, 44603, 50966, 57906, 65450, 73623, 82448, 91953, 102161, 113098, 124789, 137259, 150533, 164637, 179595, 195433
Offset: 0

Views

Author

Mohammad K. Azarian, Mar 02 2008

Keywords

Comments

Volume of a sphere of radius n, rounded up.

Links

Crossrefs

Cf. A066643, A066644, A066645, A135039.

Programs

  • Mathematica
    Table[Ceiling[4/3*Pi * n^3], {n, 0, 60}] (* Vincenzo Librandi, Feb 19 2013 *)
  • PARI
    a(n)=ceil(4/3*Pi*n^3) \\ Charles R Greathouse IV, Oct 10 2013
  • Sage
    n=100 # change n for more values
[ceil(4/3*pi*r^3) for r in [0..n]] # Tom Edgar, Oct 10 2013

Formula

a(n) = A066645(n) + 1 for n > 0.

Extensions

Definition replaced by Vincenzo Librandi, Feb 19 2013
0 prepended by T. D. Noe, Oct 10 2013

A135971 Ceiling(4*Pi*n^2).

Original entry on oeis.org

13, 51, 114, 202, 315, 453, 616, 805, 1018, 1257, 1521, 1810, 2124, 2464, 2828, 3217, 3632, 4072, 4537, 5027, 5542, 6083, 6648, 7239, 7854, 8495, 9161, 9853, 10569, 11310, 12077, 12868, 13685, 14527, 15394, 16287, 17204, 18146, 19114, 20107
Offset: 1

Views

Author

Mohammad K. Azarian, Mar 02 2008

Keywords

Comments

The original definition was "a(n)=ceiling[surface area of a shpere of radius n]".

Links

Crossrefs

Cf. A066643, A066644, A066645, A135039.

Programs

  • Mathematica
    Table[Ceiling[4 Pi n^2], {n, 1, 50}] (* Vincenzo Librandi, Feb 19 2013 *)

Extensions

Definition replaced by Bruno Berselli, Feb 19 2013

A135607 Floor of the area of a circle in terms of its circumference n.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 2, 3, 5, 6, 7, 9, 11, 13, 15, 17, 20, 22, 25, 28, 31, 35, 38, 42, 45, 49, 53, 58, 62, 66, 71, 76, 81, 86, 91, 97, 103, 108, 114, 121, 127, 133, 140, 147, 154, 161, 168, 175, 183, 191, 198, 206, 215, 223, 232, 240, 249, 258, 267, 277, 286, 296, 305, 315
Offset: 0

Views

Author

Cino Hilliard, Feb 27 2008

Keywords

Examples

			For a circle of circumference 10, the floor of the area A = floor(100/4/Pi) = 7.

Links

Crossrefs

Cf. A038130, A066643, A135039.

Programs

  • Mathematica
    Table[Floor[n^2/(4*Pi)], {n,0,25}] (* G. C. Greubel, Oct 21 2016 *)
  • PARI
    g(n) = for(c=0,n,a=c^2/4/Pi;print1(floor(a)","))
  • PARI
    a(n) = n^2\(4*Pi); \\ Michel Marcus, Oct 22 2016

Formula

Area of a circle of radius r is A = Pi*r^2. Circumference of a circle of radius r is n = 2*Pi*r. Then area in terms of the circumference n is A = n^2/(4*Pi).
Showing 1-3 of 3 results.

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