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 A245890 #10 Mar 18 2018 17:32:20 %S A245890 1,1,3,9,37,165,834,4515 %N A245890 Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 321. %C A245890 The number of labeled increasing unary-binary trees with an associated permutation avoiding 321 in the classical sense. The tree's permutation is found by recording the labels in the order in which they appear in a breadth-first search. (Note that a breadth-first search reading word is equivalent to reading the tree labels left to right by levels, starting with the root.) %C A245890 In some cases, the same breadth-first search reading permutation can be found on differently shaped trees. This sequence gives the number of trees, not the number of permutations. %H A245890 Manda Riehl, <a href="/A245890/a245890.png">The 9 trees when n=4.</a> %e A245890 When n=4, a(n)=9. In the Links above we show the nine labeled increasing trees on four nodes whose permutation avoids 321. %Y A245890 A245896 gives the number of binary trees instead of unary-binary trees. A245900 gives the number of permutations which avoid 321 that are breadth-first reading words on labeled increasing unary-binary trees. %K A245890 nonn,more %O A245890 1,3 %A A245890 _Manda Riehl_, Aug 19 2014