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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
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
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
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[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]
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
KEYWORD
nonn,easy
AUTHOR
Giovanni Resta, May 05 2017
STATUS
approved