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

Author

Rick L. Shepherd, May 29 2002

Keywords

• easy
• nonn

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

• Eric Weisstein's World of Mathematics, Tetrahedron
• Eric Weisstein's World of Mathematics, Platonic Solid

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)