A071400 Rounded volume of a regular octahedron with edge length n.

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

Author

Rick L. Shepherd, May 29 2002

Keywords

• easy
• nonn

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)