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.

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).

A071396 Rounded total surface area of a regular octahedron with edge length n.

Original entry on oeis.org

0, 3, 14, 31, 55, 87, 125, 170, 222, 281, 346, 419, 499, 585, 679, 779, 887, 1001, 1122, 1251, 1386, 1528, 1677, 1833, 1995, 2165, 2342, 2525, 2716, 2913, 3118, 3329, 3547, 3772, 4005, 4244, 4489, 4742, 5002, 5269, 5543, 5823, 6111, 6405, 6707, 7015, 7330
Offset: 0

Views

Author

Rick L. Shepherd, May 23 2002

Keywords

Examples

			a(3)=31 because round(2*3^2*sqrt(3)) = round(18*1.73205...) = round(31.1769...) = 31.

References

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

Links

Crossrefs

Cf. A070169 (tetrahedron), A033581 (cube), A071397 (dodecahedron), A071398 (icosahedron), A071400 (volume of octahedron).

Programs

  • Magma
    [Round(2*n^2 * Sqrt(3)): n in [0..50]]; // Vincenzo Librandi, May 21 2011
  • Mathematica
    Table[Round[2n^2 Sqrt[3]],{n,0,50}] (* Harvey P. Dale, Feb 19 2024 *)
  • PARI
    for(n=0,100,print1(round(2*n^2*sqrt(3)),","))
  • Python
    from math import isqrt
def A071396(n): return (m:=isqrt(k:=3*n**4<<2))+int(k>m*(m+1)) # Chai Wah Wu, Jun 05 2025

Formula

a(n) = round(2 * 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)
Showing 1-4 of 4 results.

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