

A071402


Rounded volume of a regular icosahedron with edge length n.


6



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
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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 5decimalplace approximation.


REFERENCES

S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, pp. 1011.


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: A100518 A125200 A175450 * A228641 A226417 A191295
Adjacent sequences: A071399 A071400 A071401 * A071403 A071404 A071405


KEYWORD

easy,nonn


AUTHOR

Rick L. Shepherd, May 29 2002


STATUS

approved



