A285934 Number of connected induced (non-null) subgraphs of the perfect binary tree of height n.

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

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[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

Adjacent sequences: A285931 A285932 A285933 * A285935 A285936 A285937

Keyword

nonn,easy

Author

Giovanni Resta, May 05 2017

Status

approved