A348851 a(n) is the number of labeled rooted ordered 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, 2, 2, 4, 8, 12, 20, 36, 72, 92, 172, 264, 456, 864, 1168, 1920, 2896, 4960, 7224, 13968, 17904, 29184, 43584, 71024, 100000, 165248, 257856, 365248, 532864, 800464, 1216960, 1794288, 2757888, 3948672, 6237280, 8489760, 12342432, 17454816, 26658048, 36949728, 56283168

Offset

1,3

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 u, v > 0 and 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 A348851

Wikipedia, Grundy's game

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A000108, A348850.

Sequence in context: A364669 A104221 A078044 * A329664 A153993 A244781

Adjacent sequences: A348848 A348849 A348850 * A348852 A348853 A348854

Keyword

nonn

Author

Rémy Sigrist, Nov 01 2021

Status

approved