A071402 Rounded volume of a regular icosahedron with edge length n.

0, 2, 17, 59, 140, 273, 471, 748, 1117, 1590, 2182, 2904, 3770, 4793, 5987, 7363, 8936, 10719, 12724, 14964, 17454, 20205, 23231, 26545, 30160, 34089, 38345, 42942, 47893, 53209, 58906, 64995, 71490, 78404, 85749, 93540, 101789, 110509

Offset

0,2

Comments

The printed reference given shows in a table on p. 10 that Volume is "2.18170a^3" (a is edge). Both PARI (see Example here) and a handheld calculator show that 2.18169 is correct for a 5-decimal-place approximation.

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Icosahedron

Formula

a(n) = round(n^3 * (3+sqrt(5)) * 5/12).

Example

a(6)=471 because round(6^3*(3 + sqrt(5))*5/12) = round(216*2.181694990...) = round(471.24...) = 471.

Prog

(PARI) for(n=0, 100, print1(round(n^3*(3+sqrt(5))*5/12), ", "))
(Magma) [Round(n^3 * (3+Sqrt(5)) * 5/12): n in [0..50]]; // Vincenzo Librandi, May 21 2011

Crossrefs

Cf. A000578 (cube), A071399 (tetrahedron), A071400 (octahedron), A071401 (dodecahedron), A071398 (total surface area of icosahedron).

Cf. A102208 ((3+Sqrt(5)) * 5/12).

Sequence in context: A125200 A368390 A175450 * A228641 A226417 A191295

Adjacent sequences: A071399 A071400 A071401 * A071403 A071404 A071405

Keyword

easy,nonn

Author

Rick L. Shepherd, May 29 2002

Status

approved