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.

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)

A071402 Rounded volume of a regular icosahedron with edge length n.

Original entry on oeis.org

0, 2, 17, 59, 140, 273, 471, 748, 1117, 1590, 2182, 2904, 3770, 4793, 5987, 7363, 8936, 10719, 12724, 14964, 17454, 20205, 23231, 26545, 30160, 34089, 38345, 42942, 47893, 53209, 58906, 64995, 71490, 78404, 85749, 93540, 101789, 110509
Offset: 0

Views

Author

Rick L. Shepherd, May 29 2002

Keywords

Comments

The printed reference given shows in a table on p. 10 that Volume is "2.18170a^3" (a is edge). Both PARI (see Example here) and a handheld calculator show that 2.18169 is correct for a 5-decimal-place approximation.

Examples

			a(6)=471 because round(6^3*(3 + sqrt(5))*5/12) = round(216*2.181694990...) = round(471.24...) = 471.

References

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

Links

Crossrefs

Cf. A000578 (cube), A071399 (tetrahedron), A071400 (octahedron), A071401 (dodecahedron), A071398 (total surface area of icosahedron).
Cf. A102208 ((3+Sqrt(5)) * 5/12).

Programs

  • Magma
    [Round(n^3 * (3+Sqrt(5)) * 5/12): n in [0..50]]; // Vincenzo Librandi, May 21 2011
  • PARI
    for(n=0,100,print1(round(n^3*(3+sqrt(5))*5/12),","))

Formula

a(n) = round(n^3 * (3+sqrt(5)) * 5/12).

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))).

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)

A172526 a(n)=floor(3*n^2*(2+sqrt(3))).

Original entry on oeis.org

11, 44, 100, 179, 279, 403, 548, 716, 906, 1119, 1354, 1612, 1892, 2194, 2519, 2866, 3235, 3627, 4041, 4478, 4937, 5418, 5922, 6448, 6997, 7568, 8161, 8777, 9415, 10076, 10759, 11464, 12192, 12942, 13715, 14510, 15327, 16167, 17029, 17913, 18820
Offset: 1

Views

Author

Vincenzo Librandi, Feb 06 2010

Keywords

Comments

Approximate area of the dodecahedron of side n=(1,2,3,4,...).

Links

Crossrefs

Cf. A071401.

Programs

  • Magma
    [Floor(3*n^2*(2+Sqrt(3))): n in [1..50]]; // Vincenzo Librandi, Aug 20 2014
  • Mathematica
    With[{c=3(2+Sqrt[3])},Floor[c Range[50]^2]]  (* Harvey P. Dale, Apr 01 2011 *)
f[n_]:=Floor[3 n^2 (2 + Sqrt[3])]; Array[f, 50, 1] (* Vincenzo Librandi, Aug 20 2014 *)
Showing 1-5 of 5 results.

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