A071402 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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