cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A234729 #18 Sep 26 2024 15:08:35
%S A234729 0,6,23,55,108,187,297,443,631,866,1152,1496,1902,2376,2922,3547,4254,
%T A234729 5050,5940,6928,8020,9221,10536,11971,13531,15221,17045,19010,21121,
%U A234729 23382,25799,28377,31122,34038,37130,40405,43866,47520,51371,55425,59687
%N A234729 Volume of right regular hexagonal pyramid with height and side lengths n, rounded down.
%H A234729 Georg Fischer, <a href="/A234729/b234729.txt">Table of n, a(n) for n = 1..1000</a> [first 143 terms from _K. D. Bajpai_]
%F A234729 a(n) = floor(n^2*evalf(sqrt(3)*3/2)*n/3) = floor(0.8660254040* n^3).
%e A234729 a(7) = 297: Volume = n^2 * evalf(sqrt(3)*3/2)* n/3  = 297.0467136 and floor(297.0467136) = 297.
%p A234729 a:= n-> floor(sqrt(3*n^6/4)):
%p A234729 seq(a(n), n=1..100);
%t A234729 Table[Floor[k^3*0.8660254040],{k,1,100}]
%t A234729 Table[Floor[(Sqrt[3] n^3)/2],{n,100}] (* _Harvey P. Dale_, Apr 11 2020 *)
%o A234729 (PARI) a(n)=sqrtint(3*n^6\4) \\ _Charles R Greathouse IV_, Jan 08 2014
%Y A234729 Cf. A229063 (volume of square pyramid).
%K A234729 nonn,easy
%O A234729 1,2
%A A234729 _K. D. Bajpai_, Dec 30 2013