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

%I A171163 #16 Aug 29 2025 16:04:57
%S A171163 0,2,2,4,16,256,65536,4294967296,18446744073709551616,
%T A171163 340282366920938463463374607431768211456,
%U A171163 115792089237316195423570985008687907853269984665640564039457584007913129639936
%N A171163 Number of children at height n in a doubly logarithmic tree. Leaves are at height 0.
%H A171163 Vincenzo Librandi, <a href="/A171163/b171163.txt">Table of n, a(n) for n = 0..13</a>
%H A171163 Omer Berkman, Baruch Schieber and Uzi Vishkin, <a href="https://doi.org/10.1006/jagm.1993.1018">Optimal doubly logarithmic parallel algorithms based on finding all nearest smaller values</a>, Journal of Algorithms, 14(1993)(3): 344-370.
%F A171163 a(0)=0, a(1)=2; for n>1, a(n) = 2^(2^(n-2)).
%t A171163 Join[{0, 2}, Table[2^2^(n-2), {n, 2, 9}]] (* _Harvey P. Dale_, Feb 01 2014 *)
%o A171163 (Python)
%o A171163 def doubly_log_tree_children(n):
%o A171163     if n==0:
%o A171163         return 0
%o A171163     if n==1:
%o A171163         return 2
%o A171163     return 2**(2**(n-2))
%Y A171163 Equals A001146 with the prefix 0, 2.
%Y A171163 Essentially the same as A165420.
%K A171163 nonn,changed
%O A171163 0,2
%A A171163 _Chad Brewbaker_, Dec 04 2009
%E A171163 More terms from _Harvey P. Dale_, Feb 01 2014