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

0,3

References

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

Links

Table of n, a(n) for n=0..41.

Eric Weisstein's World of Mathematics, Octahedron

Formula

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

Example

a(4)=30 because round(4^3*sqrt(2)/3)=round(64*.47140...)=round(30.169...)=30.

Mathematica

With[{c=Sqrt[2]/3}, Table[Round[n^3*c], {n, 0, 50}]] (* Harvey P. Dale, May 20 2014 *)

Prog

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

Crossrefs

Cf. A000578 (cube), A071399 (tetrahedron), A071401 (dodecahedron), A071402 (icosahedron), A071396 (total surface area of octahedron).

Sequence in context: A041301 A138989 A254830 * A206806 A022913 A232228

Adjacent sequences: A071397 A071398 A071399 * A071401 A071402 A071403

Keyword

easy,nonn

Author

Rick L. Shepherd, May 29 2002

Status

approved