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.
%I A050293 #23 Feb 16 2025 08:32:40
%S A050293 1,2,4,6,12,24,36,72,144,240,480,960,1440,2880,5760,8640,17280,34560,
%T A050293 57600,115200,230400,345600,691200,1382400,2073600,4147200,8294400,
%U A050293 13271040,26542080,53084160,79626240,159252480,318504960,477757440,955514880,1911029760
%N A050293 Number of 3-fold-free subsets of {1, 2, ..., n}.
%C A050293 A set is 3-fold-free if it does not contain any subset of the form {x, 3x}.
%D A050293 B. Reznick and R. Holzsager, r-fold free sets of positive integers, Math. Magazine 68 (1995) 71-72.
%H A050293 Alois P. Heinz, <a href="/A050293/b050293.txt">Table of n, a(n) for n = 0..3789</a>
%H A050293 Steven R. Finch, <a href="/FinchTriple.html">Triple-Free Sets of Integers</a> [From Steven Finch, Apr 20 2019]
%H A050293 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Triple-FreeSet.html">Triple-Free Set.</a>
%e A050293 a(6) = 36. There are 64 subsets of {1, 2, 3, 4, 5, 6}. We exclude the 16 that contain {1, 3} and the 16 that contain {2, 6}. We've double-counted the 4 that contain {1, 2, 3, 6}. This yields 64 - 16 - 16 + 4 = 36.
%Y A050293 Cf. A050291-A050296, A068060.
%K A050293 nonn
%O A050293 0,2
%A A050293 _Eric W. Weisstein_
%E A050293 More terms from _David Wasserman_, Feb 14 2002
%E A050293 Corrected and edited by _Steven Finch_, Feb 25 2009
%E A050293 a(0)=1 prepended by _Alois P. Heinz_, Jan 16 2019