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

Author

Rick L. Shepherd, May 29 2002

Keywords

• easy
• nonn

Examples

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

References

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

Links

• Eric Weisstein's World of Mathematics, Dodecahedron

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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