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 A245900 #15 Jun 04 2018 14:43:44 %S A245900 1,1,2,4,10,27,79,239 %N A245900 Number of permutations of [n] avoiding 321 that can be realized on increasing unary-binary trees. %C A245900 The number of permutations avoiding 321 in the classical sense which can be realized as labels on an increasing unary-binary tree read in the order they appear in a breadth-first search. (Note that breadth-first search reading word is equivalent to reading the tree left to right by levels, starting with the root.) %C A245900 In some cases, more than one tree results in the same breadth-first search reading word, but here we count the permutations, not the trees. %e A245900 For example, when n=4, a(n)=4. The permutations 1234, 1243, 1324, and 1423 all avoid 321 in the classical sense and occur as breadth-first search reading words on an increasing unary-binary tree with 4 nodes: %e A245900 1 1 1 1 %e A245900 / \ / \ / \ / \ %e A245900 2 3 2 4 3 2 4 2 %e A245900 | | | | %e A245900 4 3 4 3 %Y A245900 Cf. A245903 (odd bisection). %Y A245900 A245890 is the number of increasing unary-binary trees whose breadth-first reading word avoids 321. %K A245900 nonn,more %O A245900 1,3 %A A245900 _Manda Riehl_, Aug 06 2014