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

1,2

Links

K. D. Bajpai, Table of n, a(n) for n = 1..1000

Formula

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

Example

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

Maple

KD:= proc() local a, b; a:=n^2*evalf(sqrt(3)*3/2)*n/3 ; b:=floor(a); RETURN(b): end: seq(KD(), 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 *)

Prog

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

Crossrefs

Cf. A229063 (volume of square pyramid).

Sequence in context: A272840 A272941 A272922 * A273500 A189713 A162267

Adjacent sequences: A234726 A234727 A234728 * A234730 A234731 A234732

Keyword

nonn,easy

Author

K. D. Bajpai, Dec 30 2013

Status

approved