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A071401 Rounded volume of a regular dodecahedron with edge length n. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

Table of n, a(n) for n=0..35.

Eric Weisstein's World of Mathematics, Dodecahedron

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A034664 A242084 A007399 * A247535 A283852 A283410

Adjacent sequences:  A071398 A071399 A071400 * A071402 A071403 A071404

KEYWORD

easy,nonn

AUTHOR

Rick L. Shepherd, May 29 2002

STATUS

approved

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Last modified March 18 12:10 EDT 2019. Contains 321283 sequences. (Running on oeis4.)