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 A350361 #20 Nov 30 2023 07:19:25
%S A350361 4,5,5,6,6,6,7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,11,11,
%T A350361 11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,
%U A350361 13,13,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15
%N A350361 2-tone chromatic number of a tree with maximum degree n.
%C A350361 The 2-tone chromatic number of a graph G is the smallest number of colors for which G has a coloring where every vertex has two distinct colors, no adjacent vertices have a common color, and no pair of vertices at distance 2 have two common colors.
%C A350361 a(n) is also the 2-tone chromatic number of a star with n leaves.
%H A350361 A. Bickle and B. Phillips, <a href="https://allanbickle.files.wordpress.com/2016/05/ttonepaperb.pdf">t-Tone Colorings of Graphs</a>, Utilitas Math, 106 (2018) 85-102.
%H A350361 Allan Bickle, <a href="https://allanbickle.files.wordpress.com/2016/05/2tonejcpaper.pdf">2-Tone coloring of joins and products of graphs</a>, Congr. Numer. 217 (2013), 171-190.
%H A350361 N. Fonger, J. Goss, B. Phillips, and C. Segroves, <a href="https://web.archive.org/web/20220121030248/https://homepages.wmich.edu/~zhang/finalReport2.pdf">Math 6450: Final Report</a>, (2009).
%F A350361 a(n) = A003057(n-1) + 2.
%F A350361 a(n) = ceiling((5 + sqrt(1 + 8*n))/2).
%e A350361 For a star with three leaves, label the leaves 12, 13, and 23. Label the other vertex 45. A total of 5 colors are used, so a(3)=5.
%t A350361 Table[Ceiling[(5 + Sqrt[1 + 8*n])/2],{n,71}] (* _Stefano Spezia_, Dec 27 2021 *)
%Y A350361 Cf. A003057, A350362.
%K A350361 nonn,easy
%O A350361 1,1
%A A350361 _Allan Bickle_, Dec 26 2021