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

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

0,4

References

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

Links

Table of n, a(n) for n=0..47.

Eric Weisstein's World of Mathematics, Tetrahedron

Eric Weisstein's World of Mathematics, Platonic Solid

Formula

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

a(n) >= A171973(n). - R. J. Mathar, Feb 06 2026

Example

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

Mathematica

With[{c=Sqrt[2]/12}, Round[c*Range[0, 50]^3]] (* Harvey P. Dale, Feb 25 2015 *)

Prog

(PARI) for(n=0, 100, print1(round(n^3*sqrt(2)/12), ", "))

Crossrefs

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

Sequence in context: A212772 A238806 A080181 * A387529 A001208 A159465

Adjacent sequences: A071396 A071397 A071398 * A071400 A071401 A071402

Keyword

easy,nonn

Author

Rick L. Shepherd, May 29 2002

Status

approved