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A071399 Rounded volume of a regular tetrahedron with edge length n. 6
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 (list; graph; refs; listen; history; text; internal format)
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)

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 * A001208 A159465 A071148

Adjacent sequences:  A071396 A071397 A071398 * A071400 A071401 A071402

KEYWORD

easy,nonn

AUTHOR

Rick L. Shepherd, May 29 2002

STATUS

approved

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Last modified March 25 04:24 EDT 2019. Contains 321457 sequences. (Running on oeis4.)