A234729 Volume of right regular hexagonal pyramid with height and side lengths n, rounded down.

0, 6, 23, 55, 108, 187, 297, 443, 631, 866, 1152, 1496, 1902, 2376, 2922, 3547, 4254, 5050, 5940, 6928, 8020, 9221, 10536, 11971, 13531, 15221, 17045, 19010, 21121, 23382, 25799, 28377, 31122, 34038, 37130, 40405, 43866, 47520, 51371, 55425, 59687

Offset: 1

Author

K. D. Bajpai, Dec 30 2013

Keywords

• nonn
• easy

Examples

			a(7) = 297: Volume = n^2 * evalf(sqrt(3)*3/2)* n/3  = 297.0467136 and floor(297.0467136) = 297.
		

Links

• Georg Fischer, Table of n, a(n) for n = 1..1000 [first 143 terms from _K. D. Bajpai_]

Crossrefs

Cf. A229063 (volume of square pyramid).

Programs

Maple

a:= n-> floor(sqrt(3*n^6/4)):
seq(a(n), n=1..100);

Mathematica

Table[Floor[k^3*0.8660254040],{k,1,100}]
Table[Floor[(Sqrt[3] n^3)/2],{n,100}] (* Harvey P. Dale, Apr 11 2020 *)

PARI

a(n)=sqrtint(3*n^6\4) \\ Charles R Greathouse IV, Jan 08 2014

Formula

a(n) = floor(n^2*evalf(sqrt(3)*3/2)*n/3) = floor(0.8660254040* n^3).