cp's OEIS Frontend

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.

%I A348851 #10 Nov 09 2021 05:36:46
%S A348851 1,1,2,2,4,8,12,20,36,72,92,172,264,456,864,1168,1920,2896,4960,7224,
%T A348851 13968,17904,29184,43584,71024,100000,165248,257856,365248,532864,
%U A348851 800464,1216960,1794288,2757888,3948672,6237280,8489760,12342432,17454816,26658048,36949728,56283168
%N 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.
%C A348851 For any n > 0:
%C A348851 - we can imagine a variant of Grundy's game where we start with n at root position,
%C A348851 - 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,
%C A348851 - a(n) gives the number of final positions (where no move is possible).
%H A348851 Rémy Sigrist, <a href="/A348851/a348851.gp.txt">PARI program for A348851</a>
%H A348851 Wikipedia, <a href="https://en.wikipedia.org/wiki/Grundy%27s_game">Grundy's game</a>
%e A348851 For n = 1, 2: a(n) = 1:
%e A348851           |         |
%e A348851           1         2
%e A348851 For n = 3, 4: a(n) = 2:
%e A348851           |         |         |         |
%e A348851           3         3         4         4
%e A348851          / \       / \       / \       / \
%e A348851         1   2     2   1     1   3     3   1
%o A348851 (PARI) See Links section.
%Y A348851 Cf. A000108, A348850.
%K A348851 nonn
%O A348851 1,3
%A A348851 _Rémy Sigrist_, Nov 01 2021