A071401 Rounded volume of a regular dodecahedron with edge length n.

0, 8, 61, 207, 490, 958, 1655, 2628, 3924, 5586, 7663, 10200, 13242, 16836, 21028, 25863, 31388, 37649, 44691, 52561, 61305, 70968, 81597, 93237, 105935, 119736, 134687, 150833, 168221, 186896, 206904, 228292, 251105, 275390, 301191, 328556

Offset

0,2

References

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

Links

Table of n, a(n) for n=0..35.

Eric Weisstein's World of Mathematics, Dodecahedron

Formula

a(n) = round(n^3 * (15+7*sqrt(5))/4)

Example

a(6)=1665 because round(6^3*(15+7*sqrt(5))/4)=round(216*7.6631...)=round(1655.23...)=1665.

Mathematica

Table[Floor[n^3 (15+7Sqrt[5])/4+1/2], {n, 0, 50}]  (* Harvey P. Dale, Apr 25 2011 *)

Prog

(PARI) for(n=0, 100, print1(round(n^3*(15+7*sqrt(5))/4), ", "))

Crossrefs

Cf. A000578 (cube), A071399 (tetrahedron), A071400 (octahedron), A071402 (icosahedron), A071397 (total surface area of dodecahedron).

Sequence in context: A034664 A242084 A007399 * A247535 A283852 A283410

Adjacent sequences: A071398 A071399 A071400 * A071402 A071403 A071404

Keyword

easy,nonn

Author

Rick L. Shepherd, May 29 2002

Status

approved