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

1,5

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

Table of n, a(n) for n=1..31.

Washington Bomfim, Illustration of initial terms

Index entries for sequences related to rooted trees

Formula

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

Crossrefs

Cf. A253013, A253014, A339524.

Sequence in context: A370033 A244208 A296329 * A295045 A181849 A164586

Adjacent sequences: A339522 A339523 A339524 * A339526 A339527 A339528

Keyword

nonn

Author

Washington Bomfim, Dec 08 2020

Status

approved