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.

A171973 Integer part of the volume of a regular tetrahedron with edge length n.

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%I A171973 #9 Feb 16 2025 08:33:11
%S A171973 0,0,3,7,14,25,40,60,85,117,156,203,258,323,397,482,579,687,808,942,
%T A171973 1091,1254,1433,1629,1841,2071,2319,2587,2874,3181,3510,3861,4235,
%U A171973 4632,5052,5498,5969,6466,6990,7542,8122,8731,9369,10039,10739,11471,12235
%N A171973 Integer part of the volume of a regular tetrahedron with edge length n.
%C A171973 Lim{n->oo} a(n)/A000292(n) = sqrt(2)/2;
%C A171973 floor(A171971(n)*A171974(n)/3) <= a(n).
%H A171973 Reinhard Zumkeller, <a href="/A171973/b171973.txt">Table of n, a(n) for n = 1..1000</a>
%H A171973 Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetrahedron">Tetrahedron</a>
%H A171973 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Tetrahedron.html">Tetrahedron</a>
%F A171973 a(n) = floor(n^3 * sqrt(2) / 12).
%o A171973 (Haskell)
%o A171973 a171973 = floor . (/ 12) . (* sqrt 2) . fromInteger . a000578
%o A171973 -- _Reinhard Zumkeller_, Dec 15 2012
%Y A171973 Cf. A001951, A171972, A171975, A000578.
%K A171973 nonn
%O A171973 1,3
%A A171973 _Reinhard Zumkeller_, Jan 20 2010