A287211
The number of plane rooted complete ternary trees with 2n+1 unlabeled leaves (hence n internal nodes including the root where n starts at 0) satisfying these two conditions: (1) if one of the three children of any internal node is the greatest in deglex order then that child is not the leftmost child; (2) if one of the three children of any internal node is the smallest in deglex order then that child is not the rightmost child. Deglex order refers to degree-lexicographical order defined inductively on the number of leaves (see details under Comments).
| n |
a(n) |
| 0 |
1 |
| 1 |
1 |
| 2 |
2 |
| 3 |
6 |
| 4 |
21 |
| 5 |
78 |
| 6 |
308 |
| 7 |
1264 |
| 8 |
5332 |
| 9 |
22994 |
| 10 |
100896 |
| 11 |
449004 |
[1, 1, 2, 6, 21, 78, 308, 1264, 5332, 22994, 100896, 449004]