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