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 A383998 #21 Aug 12 2025 14:06:35
%S A383998 1,1,1,2,3,6,11,20,37,68,114,188,300,462,702,1041
%N A383998 Number of distinct truncated Graham sequences (as in Graham's Tree Reconstruction Conjecture) of length 4 on trees of order n.
%C A383998 For small trees, the sequence |G|, |L(G)|, |L(L(G))|, |L(L(L(G)))| is sufficient to determine the tree, so this sequence has the same first few terms as A000055.
%H A383998 Kaylee Weatherspoon, <a href="/A383998/a383998.txt">Maple program</a>.
%H A383998 Kaylee Weatherspoon and Doron Zeilberger, <a href="https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/treeline.html">An Experimental Note on Graham’s Tree Reconstruction Conjecture</a>, Rutgers Univ. (2025). See p. 3.
%e A383998 For n=8, there are 23 trees but only 20 distinct truncated Graham sequences of length 4.
%e A383998 There are two pairs of trees on 8 vertices which have the same length-4 sequence [|G|, |L(G)|, |L(L(G))|, |L(L(L(G)))|], namely the sequence [8,7,7,9] which comes from both the (unlabeled versions of) {{1, 2}, {2, 3}, {3, 7}, {4, 5}, {5, 6}, {6, 7}, {7, 8}} and {{1, 2}, {2, 3}, {3, 8}, {4, 7}, {5, 6}, {6, 7}, {7, 8}}.
%e A383998 But for sequences of length 5 there are different sequences, namely
%e A383998 [8, 7, 7, 9, 18] and [8, 7, 7, 9, 17]: the sequence [8,7,9,17] comes from both {{1, 3}, {2, 3}, {3, 7}, {4, 6}, {5, 6}, {6, 7}, {7, 8}} and {{1, 2}, {2, 3}, {3, 8}, {4, 7}, {5, 7}, {6, 7}, {7, 8}}
%e A383998 So Graham's conjecture is confirmed for trees with 8 vertices, but requires using sequences of length up to 5.
%Y A383998 Cf. A000055.
%K A383998 nonn,more
%O A383998 1,4
%A A383998 _Kaylee Weatherspoon_, May 22 2025
%E A383998 Corrected by _Doron Zeilberger_, Aug 12 2025.