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Search: id:A071402
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| A071402 |
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Rounded volume of a regular icosahedron with edge length n. |
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+0
5
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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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.
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REFERENCES
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S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, pp. 10-11.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics
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FORMULA
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a(n) = round(n^3 * (3+sqrt(5)) * 5/12)
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EXAMPLE
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a(6)=471 because round(6^3*(3+sqrt(5))*5/12)=round(216*2.181694990...)=round(471.24...)=471.
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PROGRAM
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(PARI) for(n=0, 100, print1(round(n^3*(3+sqrt(5))*5/12), ", "))
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CROSSREFS
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Cf. A000578 (cube), A071399 (tetrahedron), A071400 (octahedron), A071401 (dodecahedron), A071398 (total surface area of icosahedron).
Sequence in context: A125609 A100518 A125200 this_sequence A002430 A160469 A037420
Adjacent sequences: A071399 A071400 A071401 this_sequence A071403 A071404 A071405
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KEYWORD
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easy,nonn
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AUTHOR
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Rick L. Shepherd (rshepherd2(AT)hotmail.com), May 29 2002
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