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 A285934 Number of connected induced (non-null) subgraphs of the perfect binary tree of height n. 3
 1, 6, 37, 750, 459829, 210067308558, 44127887746326310604917, 1947270476915296449559791701269341583074001038 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A perfect (sometimes called complete) binary tree of height k has 2^(k+1)-1 nodes. a(8) has 91 digits and thus it is not reported. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..11 Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph Wikipedia, Types of binary trees FORMULA 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). MATHEMATICA a=b=1; b[n_] := b[n] = 1 + b[n - 1]^2; a[n_] := a[n] = b[n]^2 + 2 a[n - 1]; Array[a, 8] CROSSREFS 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). Sequence in context: A240324 A283636 A211988 * A083373 A320988 A015492 Adjacent sequences:  A285931 A285932 A285933 * A285935 A285936 A285937 KEYWORD nonn,easy AUTHOR Giovanni Resta, May 05 2017 STATUS approved

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Last modified May 18 03:30 EDT 2022. Contains 353783 sequences. (Running on oeis4.)