A339525 Number of unordered pairs of rooted trees with a total of n nodes and an odd total of leaves.

0, 0, 0, 1, 3, 8, 19, 47, 119, 309, 805, 2115, 5594, 14920, 40037, 108068, 293124, 798739, 2185380, 6001797, 16538728, 45716315, 126727586, 352214041, 981269274, 2739925455, 7666335708, 21491822234, 60358497108, 169798015580, 478420350367

Offset: 1

Author

Washington Bomfim, Dec 08 2020

Keywords

• nonn

Comments

Equivalently, the number of rooted trees on n+1 nodes, where the root has degree 2, and the number of leaves is odd.

To get a pair of trees with an odd number of leaves one tree must have an even number of leaves and the other an odd number of leaves.

Links

• Washington Bomfim, Illustration of initial terms
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A253013, A253014, A339524.

Formula

a(n) = Sum_{k=1, n-1}( A253013(k) * A253014(n-k) ).