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 A177407 #35 Feb 10 2023 11:55:26 %S A177407 1,1,1,3,3,1,1,5,7,3,9,9,3,7,5,1,1,7,11,5,17,19,7,17,13,3,5,7,9,27,27, %T A177407 9,7,5,3,13,17,7,19,17,5,11,7,1,1,9,15,7,25,29,11,27,21,5,9,13,17,53, %U A177407 55,19,15,11,7,31,41,17,47,43,13,29,19,3,11,13,5,17,19,7,23,25,9 %N A177407 Form triangle of weighted Farey fractions; read denominators by rows. %C A177407 Start with the list of fractions 0/1, 1/1 and repeatedly insert the weighted mediants (2a+c)/(2b+d) and (a+2c)/(b+2d) between every pair of adjacent elements a/b and c/d of the list. The fractions are to be reduced before the insertion step. %D A177407 James Propp, Posting to the Math Fun Mailing List, Dec 10 2010. %H A177407 Nathaniel Johnston, <a href="/A177407/b177407.txt">Table of n, a(n) for n = 0..29533</a> (first 10 rows of triangle) %H A177407 Dhroova Aiylam and Tanya Khovanova, <a href="https://arxiv.org/abs/1711.01475">Weighted Mediants and Fractals</a>, arXiv:1711.01475 [math.NT], 2017. %e A177407 Triangle begins: %e A177407 0 1 %e A177407 - - %e A177407 1 1 %e A177407 . %e A177407 0 1 2 1 %e A177407 - - - - %e A177407 1 3 3 1 %e A177407 . %e A177407 0 1 2 1 4 5 2 5 4 1 %e A177407 - - - - - - - - - - %e A177407 1 5 7 3 9 9 3 7 5 1 %Y A177407 Cf. A177405, A177903, A006842/A006843. %K A177407 nonn,frac,tabf,easy %O A177407 0,4 %A A177407 _N. J. A. Sloane_, Dec 10 2010 %E A177407 a(44)-a(80) and some corrected terms from _Nathaniel Johnston_, Apr 12 2011