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 A245899 #23 Dec 11 2019 07:35:06 %S A245899 1,1,2,3,7,14,37,80 %N A245899 a(n) is the number of permutations avoiding 312 that can be realized on increasing unary-binary trees with n nodes. %C A245899 The number of permutations avoiding 312 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 A245899 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. %H A245899 D. Levin, L. Pudwell, M. Riehl, A. Sandberg, <a href="http://www.etsu.edu/cas/math/pp2014/documents/talks/riehl.pdf">Pattern Avoidance on k-ary Heaps</a>, Slides of Talk, 2014. %e A245899 For example, when n=4, a(n)=3. The permutations 1234, 1243, and 1324 all avoid 312 in the classical sense and occur as breadth-first search reading words on an increasing unary-binary tree with 4 nodes: %e A245899 1 1 1 %e A245899 / \ / \ / \ %e A245899 2 3 2 4 3 2 %e A245899 | | | %e A245899 4 3 4 %Y A245899 A245902 appears to be the odd-indexed terms of this sequence. %Y A245899 Cf. A245889 (the number of increasing unary-binary trees whose breadth-first reading word avoids 312). %K A245899 nonn,more %O A245899 1,3 %A A245899 _Manda Riehl_, Aug 06 2014