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 A285934 #16 Feb 16 2025 08:33:44 %S A285934 1,6,37,750,459829,210067308558,44127887746326310604917, %T A285934 1947270476915296449559791701269341583074001038 %N A285934 Number of connected induced (non-null) subgraphs of the perfect binary tree of height n. %C A285934 A perfect (sometimes called complete) binary tree of height k has 2^(k+1)-1 nodes. %C A285934 a(8) has 91 digits and thus it is not reported. %H A285934 Alois P. Heinz, <a href="/A285934/b285934.txt">Table of n, a(n) for n = 0..11</a> %H A285934 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</a> %H A285934 Wikipedia, <a href="https://en.wikipedia.org/wiki/Binary_tree#Types_of_binary_trees">Types of binary trees</a> %F A285934 Let b(0)=1 and b(n) = 1+b(n-1)^2. Then, a(0)=1 and a(n) = b(n)^2 + 2*a(n-1). Note that b(n) = A003095(n+1). %t A285934 a[1]=b[1]=1; b[n_] := b[n] = 1 + b[n - 1]^2; a[n_] := a[n] = b[n]^2 + 2 a[n - 1]; Array[a, 8] %Y A285934 Cf. A003095, A020873 (wheel), A059020 (ladder), A059525 (grid), A286139 (king), A286182 (prism), A286183 (antiprism), A286184 (helm), A286185 (Möbius ladder), A286186 (friendship), A286187 (web), A286188 (gear), A286189 (rook), A285765 (queen). %K A285934 nonn,easy %O A285934 0,2 %A A285934 _Giovanni Resta_, May 05 2017