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A071400 Rounded volume of a regular octahedron with edge length n. 4
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 (list; graph; refs; listen; history; text; internal format)
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 A232228 A218213

Adjacent sequences:  A071397 A071398 A071399 * A071401 A071402 A071403

KEYWORD

easy,nonn

AUTHOR

Rick L. Shepherd, May 29 2002

STATUS

approved

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Last modified June 25 11:52 EDT 2017. Contains 288710 sequences.