A228272 -id:A228272 - cp's OEIS frontend

A228641 Volume of torus (rounded down) with major radius = n and minor radius = n/3.

2, 17, 59, 140, 274, 473, 752, 1122, 1598, 2193, 2919, 3789, 4818, 6018, 7402, 8983, 10775, 12791, 15043, 17545, 20311, 23353, 26685, 30319, 34269, 38548, 43169, 48146, 53491, 59217, 65338, 71868, 78818, 86203, 94035, 102328, 111094, 120347, 130101, 140367, 151160

Offset: 1

K. D. Bajpai, Aug 28 2013

nonn

			a(6) = 473 :  volume = ((2  *Pi * n) * (Pi * (n/3)^2)) = ((2 *Pi * 6) * (Pi * (6/3)^2)) = 473.7410114 and floor(473.7410114) =  473.

K. D. Bajpai, Table of n, a(n) for n = 1..100
Wikipedia, Torus

Cf. A228272.

KD := proc() local a; a:=floor( evalf( (2*Pi*n)*(Pi*(n/3)^2) ) ); RETURN (a) :end: seq(KD(),n=1..50);

a(n)=floor(2/9*Pi^2*n^3) \\ Charles R Greathouse IV, Aug 28 2013

a(n) = floor( 2/9 * Pi^2 * n^3 ).

A273264 Volume of unit n-ball, rounded to the nearest integer.

Original entry on oeis.org

2, 3, 4, 5, 5, 5, 5, 4, 3, 3, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Felix Fröhlich, May 18 2016

			The volume of the unit 3-ball (the set of points of distance equal to or less than the radius of the midpoint of the ordinary sphere or 2-sphere) is equal to 4/3*Pi, which is 4.1887902047... (A019699) and when rounded down this is 4, so a(3) = 4.

Wikipedia, Volume of an n-ball.

Cf. A019699, A177677, A228272.

Table[Round[(Pi^(n/2))/Gamma[1 + n/2]], {n, 120}] (* Michael De Vlieger, May 19 2016 *)

a(n) = round((Pi^(n/2)) / (gamma(1+n/2)))

a(n) = round((Pi^(n/2)) / (Gamma(1 + n/2))).

cp's OEIS Frontend

A228641 Volume of torus (rounded down) with major radius = n and minor radius = n/3.

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