A348850 - OEIS

A348850

a(n) is the number of labeled rooted unordered binary trees T where the nodes are labeled with distinct positive integers, the root has label n, each parent label equals the sum of its children labels, and T cannot be extended.

1, 1, 1, 1, 2, 2, 3, 5, 9, 10, 14, 22, 33, 57, 66, 94, 132, 188, 317, 454, 576, 806, 1083, 1535, 2342, 3215, 5231, 5656, 8545, 10804, 15226, 21153, 30342, 44536, 63165, 73877, 107241, 133994, 178497, 247564, 331695, 472331

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

For any n > 0:

- we can imagine a variant of Grundy's game where we start with n at root position,

- and each move consists in adding to a leaf, say w, two children, u and v such that 0 < u < v and u+v = w and u and v do not already appear in the tree,

- a(n) gives the number of final positions (where no move is possible).

LINKS

Table of n, a(n) for n=1..42.

Rémy Sigrist, PARI program for A348850

Wikipedia, Grundy's game

EXAMPLE

For n = 1, 2, 3, 4: a(n) = 1:

| | | |

1 2 3 4

/ \ / \

1 2 1 3

For n = 5, 6: a(n) = 2: