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 A377936 #20 Nov 15 2024 09:03:34
%S A377936 2,4,24,720,712800,666860040000,597568733024952150000000,
%T A377936 474258018883889933710067708314342382812500000000
%N A377936 Number of matchings in the complete planted binary tree with 2^n leaves.
%C A377936 A planted binary tree has an initial root node with 1 child. The root is not considered to be a leaf. All internal nodes have degree 3. The total number of nodes is 2*n.
%H A377936 Andrew Howroyd, <a href="/A377936/b377936.txt">Table of n, a(n) for n = 0..11</a>
%H A377936 Atabey Kaygun <a href="https://kaygun.github.io/clean/2024-11-12-balanced-trees.html">Hosoya Index of Balanced Binary Trees</a>.
%H A377936 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentEdgeSet.html">Independent Edge Set</a>.
%H A377936 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Matching.html">Matching</a>.
%F A377936 a(n) = u(n) + v(n) where u(n) = v(n-1)^2 and v(n) = v(n-1)^2 + 2*v(n-1)*u(n-1) with u(1) = v(1) = 1. - _Andrew Howroyd_, Nov 14 2024
%e A377936 The initial graphs for n=0..2 are:
%e A377936 o o o
%e A377936 | | |
%e A377936 o o o
%e A377936 / \ / \
%e A377936 o o o o
%e A377936 / \ / \
%e A377936 o o o o
%o A377936 (PARI) lista(n)={my(u=vector(n), v=vector(n)); u[1]=v[1]=1; for(n=1, #u-1, u[n+1]=v[n]^2; v[n+1]=u[n+1] + 2*v[n]*u[n]); v+u} \\ _Andrew Howroyd_, Nov 14 2024
%Y A377936 Cf. A338293.
%K A377936 nonn
%O A377936 0,1
%A A377936 _Atabey Kaygun_, Nov 11 2024
%E A377936 a(5) onwards from _Andrew Howroyd_, Nov 14 2024