This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A348850 #12 Nov 21 2021 09:54:22 %S A348850 1,1,1,1,2,2,3,5,9,10,14,22,33,57,66,94,132,188,317,454,576,806,1083, %T A348850 1535,2342,3215,5231,5656,8545,10804,15226,21153,30342,44536,63165, %U A348850 73877,107241,133994,178497,247564,331695,472331 %N 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. %C A348850 For any n > 0: %C A348850 - we can imagine a variant of Grundy's game where we start with n at root position, %C A348850 - 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, %C A348850 - a(n) gives the number of final positions (where no move is possible). %H A348850 Rémy Sigrist, <a href="/A348850/a348850.gp.txt">PARI program for A348850</a> %H A348850 Wikipedia, <a href="https://en.wikipedia.org/wiki/Grundy%27s_game">Grundy's game</a> %e A348850 For n = 1, 2, 3, 4: a(n) = 1: %e A348850 | | | | %e A348850 1 2 3 4 %e A348850 / \ / \ %e A348850 1 2 1 3 %e A348850 For n = 5, 6: a(n) = 2: %e A348850 | | | | %e A348850 5 5 6 6 %e A348850 / \ / \ / \ / \ %e A348850 1 4 2 3 1 5 2 4 %e A348850 / \ / \ %e A348850 2 3 1 3 %o A348850 (PARI) See Links section. %Y A348850 Cf. A124973, A346523, A348851. %K A348850 nonn,more %O A348850 1,5 %A A348850 _Rémy Sigrist_, Nov 01 2021