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 1-5 of 5 results.

A102208 Decimal expansion of the volume of an icosahedron with unit edge length.

Original entry on oeis.org

2, 1, 8, 1, 6, 9, 4, 9, 9, 0, 6, 2, 4, 9, 1, 2, 3, 7, 3, 5, 0, 3, 8, 2, 2, 3, 6, 1, 9, 7, 1, 3, 6, 5, 0, 9, 8, 1, 0, 0, 2, 5, 7, 6, 4, 9, 8, 3, 8, 1, 3, 5, 7, 1, 8, 4, 4, 6, 2, 0, 7, 1, 8, 5, 5, 8, 7, 7, 1, 7, 0, 5, 2, 3, 4, 9, 0, 8, 5, 3, 7, 4, 7, 5, 6, 0, 0, 6, 0, 0, 3, 4, 9, 1, 1, 5, 9, 2, 8, 1
Offset: 1

Views

Author

Bryan Jacobs (bryanjj(AT)gmail.com), Feb 17 2005

Keywords

Examples

			2.181694990624912373503822...

References

  • Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, ยง12.4 Theorems and Formulas (Solid Geometry), p. 451.

Links

Crossrefs

Cf. A001622 (phi), A020829 (regular tetrahedron volume), A131594 (regular octahedron volume), A102769 (regular dodecahedron volume).
Cf. A071402.

Programs

Formula

Equals 5 * (3 + sqrt(5))/12.
Equals 5*phi^2/6, phi being the golden ratio. - Stanislav Sykora, Nov 23 2013

A071399 Rounded volume of a regular tetrahedron with edge length n.

Original entry on oeis.org

0, 0, 1, 3, 8, 15, 25, 40, 60, 86, 118, 157, 204, 259, 323, 398, 483, 579, 687, 808, 943, 1091, 1255, 1434, 1629, 1841, 2071, 2320, 2587, 2874, 3182, 3511, 3862, 4235, 4632, 5053, 5498, 5970, 6467, 6991, 7542, 8122, 8731, 9370, 10039, 10739, 11471, 12236
Offset: 0

Views

Author

Rick L. Shepherd, May 29 2002

Keywords

Examples

			a(4)=8 because round(4^3*sqrt(2)/12)=round(64*.11785...)=round(7.542...)=8.

References

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

Links

Crossrefs

Cf. A000578 (cube), A071400 (octahedron), A071401 (dodecahedron), A071402 (icosahedron), A070169 (total surface area of tetrahedron).

Programs

  • Mathematica
    With[{c=Sqrt[2]/12},Round[c*Range[0,50]^3]] (* Harvey P. Dale, Feb 25 2015 *)
  • PARI
    for(n=0,100,print1(round(n^3*sqrt(2)/12),","))

Formula

a(n) = round(n^3 * sqrt(2)/12)

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)).

A071401 Rounded volume of a regular dodecahedron with edge length n.

Original entry on oeis.org

0, 8, 61, 207, 490, 958, 1655, 2628, 3924, 5586, 7663, 10200, 13242, 16836, 21028, 25863, 31388, 37649, 44691, 52561, 61305, 70968, 81597, 93237, 105935, 119736, 134687, 150833, 168221, 186896, 206904, 228292, 251105, 275390, 301191, 328556
Offset: 0

Views

Author

Rick L. Shepherd, May 29 2002

Keywords

Examples

			a(6)=1665 because round(6^3*(15+7*sqrt(5))/4)=round(216*7.6631...)=round(1655.23...)=1665.

References

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

Links

Crossrefs

Cf. A000578 (cube), A071399 (tetrahedron), A071400 (octahedron), A071402 (icosahedron), A071397 (total surface area of dodecahedron).

Programs

  • Mathematica
    Table[Floor[n^3 (15+7Sqrt[5])/4+1/2],{n,0,50}]  (* Harvey P. Dale, Apr 25 2011 *)
  • PARI
    for(n=0,100,print1(round(n^3*(15+7*sqrt(5))/4),","))

Formula

a(n) = round(n^3 * (15+7*sqrt(5))/4)

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 1-5 of 5 results.

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