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Volume of right circular cone (rounded down) with the diameter of base and height equal to n.
5

%I #33 Nov 03 2024 06:16:14

%S 0,2,7,16,32,56,89,134,190,261,348,452,575,718,883,1072,1286,1526,

%T 1795,2094,2424,2787,3185,3619,4090,4601,5152,5747,6385,7068,7799,

%U 8578,9408,10289,11224,12214,13260,14365,15529,16755,18043,19396,20814,22301,23856,25482

%N Volume of right circular cone (rounded down) with the diameter of base and height equal to n.

%H Georg Fischer, <a href="/A228189/b228189.txt">Table of n, a(n) for n = 1..1000</a> [first 574 terms from _K. D. Bajpai_]

%F a(n) = floor((Pi*n^3)/12).

%e a(3) = 7 because volume = ((Pi*n^2)/4)*(n/3) = ((Pi*3*3)/4)*(3/3) = 7.06858 and floor(7.06858) = 7.

%p a:= n-> floor((Pi*n^3)/12):

%p seq(a(n), n=1..48);

%t Table[Floor[(Pi n^3)/12],{n,50}] (* _Harvey P. Dale_, May 25 2019 *)

%o (PARI) a(n)=Pi*n^3\12 \\ _Charles R Greathouse IV_, Aug 25 2014

%K nonn,easy,changed

%O 1,2

%A _K. D. Bajpai_, Aug 17 2013