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 A245889 #8 Mar 18 2018 15:33:18 %S A245889 1,1,3,8,29,110,469,2119 %N A245889 Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 312. %C A245889 The number of labeled increasing unary-binary trees with an associated permutation avoiding 312 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 A245889 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 A245889 Manda Riehl, <a href="/A245889/a245889.png">The 8 trees when n = 4.</a> %e A245889 When n=4, a(n)=8. In the Links above we show the eight labeled increasing trees on four nodes whose permutation avoids 312. %Y A245889 A245895 gives the number of binary trees instead of unary-binary trees. A245899 gives the number of permutations which avoid 312 that are breadth-first reading words on labeled increasing unary-binary trees. %K A245889 nonn,more %O A245889 1,3 %A A245889 _Manda Riehl_, Aug 18 2014