A171163 Number of children at height n in a doubly logarithmic tree. Leaves are at height 0.

0, 2, 2, 4, 16, 256, 65536, 4294967296, 18446744073709551616, 340282366920938463463374607431768211456, 115792089237316195423570985008687907853269984665640564039457584007913129639936

Offset: 0

Author

Chad Brewbaker, Dec 04 2009

Keywords

• nonn
• changed

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..13
• Omer Berkman, Baruch Schieber and Uzi Vishkin, Optimal doubly logarithmic parallel algorithms based on finding all nearest smaller values, Journal of Algorithms, 14(1993)(3): 344-370.

Crossrefs

Equals A001146 with the prefix 0, 2.

Essentially the same as A165420.

Programs

Mathematica

Join[{0, 2}, Table[2^2^(n-2), {n, 2, 9}]] (* Harvey P. Dale, Feb 01 2014 *)

Python

def doubly_log_tree_children(n):
    if n==0:
        return 0
    if n==1:
        return 2
    return 2**(2**(n-2))

Formula

a(0)=0, a(1)=2; for n>1, a(n) = 2^(2^(n-2)).

Extensions

More terms from Harvey P. Dale, Feb 01 2014