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 1-4 of 4 results.

A070169 Rounded total surface area of a regular tetrahedron with edge length n.

Original entry on oeis.org

0, 2, 7, 16, 28, 43, 62, 85, 111, 140, 173, 210, 249, 293, 339, 390, 443, 501, 561, 625, 693, 764, 838, 916, 998, 1083, 1171, 1263, 1358, 1457, 1559, 1665, 1774, 1886, 2002, 2122, 2245, 2371, 2501, 2634, 2771, 2912, 3055, 3203, 3353, 3507, 3665, 3826, 3991
Offset: 0

Views

Author

Rick L. Shepherd, Apr 24 2002

Keywords

Comments

a(n) is the integer k that minimizes |k/n^2 - sqrt(3)|. - Clark Kimberling, Oct 11 2017

Examples

			a(3)=16 because round(3^2*sqrt(3)) = round(9*1.73205...) = round(15.5884...) = 16.

References

  • S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, pp. 10-11.

Links

Crossrefs

Cf. A033581 (cube), A071396 (octahedron), A071397 (dodecahedron), A071398 (icosahedron), A071399 (volume of tetrahedron).

Programs

  • Magma
    [Round(n^2 * Sqrt(3)): n in [0..50]]; // Vincenzo Librandi, May 21 2011
  • Mathematica
    Round[Sqrt[3]#]&/@(Range[0,50]^2) (* Harvey P. Dale, Sep 24 2012 *)
  • PARI
    for(n=0,100,print1(round(n^2*sqrt(3)),","))
  • Python
    from math import isqrt
def A070169(n): return (m:=isqrt(k:=3*n**4))+(k-m*(m+1)>=1) # Chai Wah Wu, Jun 19 2024

Formula

a(n) = round(n^2 * sqrt(3)).
a(n) = A000194(3*n^4). - Christian Krause, Aug 04 2021; corrected by Chai Wah Wu, Jun 19 2024

A071397 Rounded total surface area of a regular dodecahedron with edge length n.

Original entry on oeis.org

0, 21, 83, 186, 330, 516, 743, 1012, 1321, 1672, 2065, 2498, 2973, 3489, 4047, 4645, 5285, 5967, 6689, 7453, 8258, 9105, 9993, 10922, 11892, 12904, 13957, 15051, 16186, 17363, 18581, 19841, 21141, 22483, 23866, 25291, 26757, 28264, 29812
Offset: 0

Views

Author

Rick L. Shepherd, May 28 2002

Keywords

Examples

			a(4)=330 because round(3*4^2*sqrt(25 + 10*sqrt(5))) = round(48*6.88190...) = round(330.331...) = 330.

References

  • S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, pp. 10-11.

Links

Crossrefs

Cf. A070169 (tetrahedron), A033581 (cube), A071396 (octahedron), A071398 (icosahedron), A071401 (volume of dodecahedron).

Programs

  • Magma
    [Round(3 * n^2 * Sqrt(25+10*Sqrt(5))): n in [0..50]]; // Vincenzo Librandi, May 21 2011
  • Mathematica
    With[{c=3*Sqrt[25+10*Sqrt[5]]},Round[c*Range[0,40]^2]] (* Harvey P. Dale, Jul 06 2018 *)
  • PARI
    for(n=0,100,print1(round(3*n^2*sqrt(25+10*sqrt(5))),","))

Formula

a(n) = round(3 * n^2 * sqrt(25 + 10*sqrt(5))).

A071398 Rounded total surface area of a regular icosahedron with edge length n.

Original entry on oeis.org

0, 9, 35, 78, 139, 217, 312, 424, 554, 701, 866, 1048, 1247, 1464, 1697, 1949, 2217, 2503, 2806, 3126, 3464, 3819, 4192, 4581, 4988, 5413, 5854, 6313, 6790, 7283, 7794, 8323, 8868, 9431, 10011, 10609, 11224, 11856, 12505, 13172, 13856, 14558, 15277
Offset: 0

Views

Author

Rick L. Shepherd, May 29 2002

Keywords

Examples

			a(4)=139 because round(5*4^2*sqrt(3)) = round(80*1.73205...) = round(138.56...) = 139.

References

  • S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, pp. 10-11.

Links

Crossrefs

Cf. A070169 (tetrahedron), A033581 (cube), A071396 (octahedron), A071397 (dodecahedron), A071402 (volume of icosahedron).

Programs

  • Magma
    [Round(5 * n^2 * Sqrt(3)): n in [0..50]]; // Vincenzo Librandi, May 21 2011
  • Mathematica
    With[{c=5Sqrt[3]},Round[c Range[0,50]^2]] (* Harvey P. Dale, May 20 2011 *)
  • PARI
    for(n=0,100,print1(round(5*n^2*sqrt(3)),","))
  • Python
    from math import isqrt
def A071398(n): return (m:=isqrt(k:=75*n**4))+int(k>m*(m+1)) # Chai Wah Wu, Jun 05 2025

Formula

a(n) = round(5 * n^2 * sqrt(3)).

A071400 Rounded volume of a regular octahedron with edge length n.

Original entry on oeis.org

0, 0, 4, 13, 30, 59, 102, 162, 241, 344, 471, 627, 815, 1036, 1294, 1591, 1931, 2316, 2749, 3233, 3771, 4366, 5020, 5736, 6517, 7366, 8285, 9279, 10348, 11497, 12728, 14044, 15447, 16941, 18528, 20211, 21994, 23878, 25867, 27963, 30170, 32490
Offset: 0

Views

Author

Rick L. Shepherd, May 29 2002

Keywords

Examples

			a(4)=30 because round(4^3*sqrt(2)/3)=round(64*.47140...)=round(30.169...)=30.

References

  • S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, pp. 10-11.

Links

  • Eric Weisstein's World of Mathematics, Octahedron

Crossrefs

Cf. A000578 (cube), A071399 (tetrahedron), A071401 (dodecahedron), A071402 (icosahedron), A071396 (total surface area of octahedron).

Programs

  • Mathematica
    With[{c=Sqrt[2]/3},Table[Round[n^3*c],{n,0,50}]] (* Harvey P. Dale, May 20 2014 *)
  • PARI
    for(n=0,100,print1(round(n^3*sqrt(2)/3),","))

Formula

a(n) = round(n^3 * sqrt(2)/3)
Showing 1-4 of 4 results.

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