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 A383447 #50 Jul 09 2025 05:09:07 %S A383447 1,0,1,1,2,3,6,9,19,33,67,130,270,547,1165,2456,5314,11521,25357, %T A383447 56022,125067,280471,633490,1437340,3278912,7510503,17277697,39890262, %U A383447 92427559,214835923,500879602,1171013350,2744946654,6450077870 %N A383447 Number of "peerless" trees on n nodes. %C A383447 A "peerless" tree is an unlabeled, unrooted tree (as in A000055) with the property that if two nodes are joined by an edge then these nodes have different degrees. %C A383447 _Victor S. Miller_ reports that this sequence was first proposed on Project Euler. %C A383447 Comment from _Brendan McKay_, May 01 2025 (Start) %C A383447 The enumeration could be extended by the following argument. %C A383447 If the tree has a unique centroid (not center!) then removing the centroid gives rooted subtrees of size less than n/2. If there are two centroids, they are adjacent and removing that edge gives two rooted subtrees with exactly n/2 vertices. %C A383447 Start by making all rooted trees up to n/2 vertices which have no adjacent vertices of the same degree, not counting adjacencies of the root. Then classify them according to which degrees the root can be increased to without violating this condition for edges adjacent to the root. %C A383447 With this information the counts for n vertices can be reconstructed. In this way getting up past 60 vertices should be possible. (End) %C A383447 This sequence forms the left-most column of A383448. %H A383447 Victor Miller and others, <a href="https://groups.google.com/g/seqfan/c/M34ELQF7Ikk/">Peerless trees</a>, Seqfan, 2025. %H A383447 Project Euler, <a href="https://projecteuler.net/problem=936">Problem 936: Peerless Trees</a>. %Y A383447 Cf. A000055, A383448. %K A383447 nonn,more %O A383447 1,5 %A A383447 _N. J. A. Sloane_, May 01 2025, based on postings to the SeqFan Mailing List in April and May 2025 by _Victor S. Miller_, _Allan C. Wechsler_, _Brendan McKay_, and others %E A383447 a(1)-a(8) were computed by _Allan C. Wechsler_, Apr 30 2025, and a(9)-a(34) by _Brendan McKay_, May 02 2025.