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.

A171972 Greatest integer k such that k/n^2 < sqrt(3).

Original entry on oeis.org

0, 1, 6, 15, 27, 43, 62, 84, 110, 140, 173, 209, 249, 292, 339, 389, 443, 500, 561, 625, 692, 763, 838, 916, 997, 1082, 1170, 1262, 1357, 1456, 1558, 1664, 1773, 1886, 2002, 2121, 2244, 2371, 2501, 2634, 2771, 2911, 3055, 3202, 3353, 3507, 3665, 3826, 3990, 4158
Offset: 0

Views

Author

Reinhard Zumkeller, Jan 20 2010

Keywords

Comments

Integer part of the surface area of a regular tetrahedron with edge length n.
A171970(n)*A005843(n) <= a(n);
a(n) <= 4*A171971(n); 0 <= a(n) - 4*A171971(n) < 4.

Links

Crossrefs

Cf. A002194, A070169, A171974, A171973, A171975, A000290, A293410.

Programs

  • Haskell
    a171972 = floor . (* sqrt 3) . fromInteger . a000290
-- Reinhard Zumkeller, Dec 15 2012
  • Mathematica
    z = 120; r = Sqrt[3];
Table[Floor[r*n^2], {n, 0, z}]; (* A171972 *)
Table[Ceiling[r*n^2], {n, 0, z}]; (* A293410 *)
Table[Round[r*n^2], {n, 0, z}]; (* A070169. -  Clark Kimberling, Oct 11 2017 *)

Formula

a(n) = floor(n^2 * sqrt(3)).
a(n) = A022838(n^2);
a(n) = A293410(n) - 1 for n > 0.

A171973 Integer part of the volume of a regular tetrahedron with edge length n.

Original entry on oeis.org

0, 0, 3, 7, 14, 25, 40, 60, 85, 117, 156, 203, 258, 323, 397, 482, 579, 687, 808, 942, 1091, 1254, 1433, 1629, 1841, 2071, 2319, 2587, 2874, 3181, 3510, 3861, 4235, 4632, 5052, 5498, 5969, 6466, 6990, 7542, 8122, 8731, 9369, 10039, 10739, 11471, 12235
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 20 2010

Keywords

Comments

Lim{n->oo} a(n)/A000292(n) = sqrt(2)/2;
floor(A171971(n)*A171974(n)/3) <= a(n).

Links

Crossrefs

Cf. A001951, A171972, A171975, A000578.

Programs

  • Haskell
    a171973 = floor . (/ 12) . (* sqrt 2) . fromInteger . a000578
-- Reinhard Zumkeller, Dec 15 2012

Formula

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

A171974 Integer part of the height of a regular tetrahedron with edge length n.

Original entry on oeis.org

0, 1, 2, 3, 4, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 26, 27, 28, 29, 30, 31, 31, 32, 33, 34, 35, 35, 36, 37, 38, 39, 40, 40, 41, 42, 43, 44, 44, 45, 46, 47, 48, 48, 49, 50, 51, 52, 53, 53, 54, 55, 56, 57, 57, 58, 59
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 20 2010

Keywords

Comments

-3 <= 4*A171975(n) - 3*a(n) < 3;
a(n)*A171975(n) <= A007590(n);
floor(a(n)*A171971(n)/3) <= A171973(n).

Links

Crossrefs

Cf. A171972, A022840. Beatty sequence of A157697.
Cf. A007590, A171971, A171973, A171975.

Programs

  • Haskell
    a171974 = floor . (/ 3) . (* sqrt 6) . fromInteger
-- Reinhard Zumkeller, Dec 15 2012

Formula

a(n) = floor(n*sqrt(6)/3).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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