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 A245904 #25 Jun 09 2018 06:17:48 %S A245904 1,2,6,22,84,330,1308,5210,20796,83100,332232,1328598,5313732, %T A245904 21253620,85011864,340042246,1360158564 %N A245904 a(n) is the number of permutations avoiding 231 and 312 realizable on increasing strict binary trees with 2n-1 nodes. %C A245904 The number of permutations avoiding 231 and 312 in the classical sense which can be realized as labels on an increasing strict binary tree with 2n-1 nodes. A strict binary tree is a tree graph where each node has 0 or 2 children. The permutation is found by reading the labels 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 A245904 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 A245904 For example, when n=3, the permutations 12543, 12435, 13245, 13254, 12345,and 12354. all avoid 231 and 312 in the classical sense and occur as breadth-first search reading words on an increasing strict binary tree with 5 nodes. %e A245904 . 1 1 1 1 1 1 %e A245904 . / \ / \ / \ / \ / \ / \ %e A245904 . 2 5 2 4 3 2 3 2 2 3 2 3 %e A245904 . / \ / \ / \ / \ / \ / \ %e A245904 . 4 3 3 5 4 5 5 4 4 5 5 4 %Y A245904 A bisection of A002083. %K A245904 nonn,more %O A245904 1,2 %A A245904 _Manda Riehl_, Aug 05 2014 %E A245904 More terms from _N. J. A. Sloane_, Jul 07 2015