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Volume of torus (rounded down) with major radius = n and minor radius = n/3.
1

%I #10 Aug 29 2013 13:45:37

%S 2,17,59,140,274,473,752,1122,1598,2193,2919,3789,4818,6018,7402,8983,

%T 10775,12791,15043,17545,20311,23353,26685,30319,34269,38548,43169,

%U 48146,53491,59217,65338,71868,78818,86203,94035,102328,111094,120347,130101,140367,151160

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

%H K. D. Bajpai, <a href="/A228641/b228641.txt">Table of n, a(n) for n = 1..100</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Torus">Torus</a>

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

%e 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.

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

%o (PARI) a(n)=floor(2/9*Pi^2*n^3) \\ _Charles R Greathouse IV_, Aug 28 2013

%Y Cf. A228272.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Aug 28 2013