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
KEYWORD
nonn,easy
AUTHOR
Giovanni Resta, May 05 2017
STATUS
approved