%I A120424
%S A120424 1,3,4,5,7,12,13,19,32,35,51,86,94,90,92,91,137,228,251,365,616,673,
%T A120424 981,1654,1808,1731,2635,4366,4818,4592,4705,7001,11706,12854,12280,
%U A120424 12567,18707,31274,34344,32809,49981,82790,91376,87083,132771,219854
%N A120424 Having specified two initial terms, the "Half-Fibonacci" sequence proceeds 
               like the Fibonacci sequence, except that the terms are halved before 
               being added if they are even.
%C A120424 For sequences that are inifinitely increasing, the following are possible 
               conjectures. Half of the terms are even in the limit. There are infinitely 
               many consecutive pairs that differ by 1.
%C A120424 This is essentially a variant of the Collatz - Fibonacci mixture described 
               in A069202. Instead of conditionally dividing the result by 2, this 
               sequence conditionally divides the two previous terms by 2. The initial 
               two terms of A069202 are 1,2, which corresponds to the initial terms 
               1,4 for this sequence.
%F A120424 a(n) = (a(n-1) if a(n-1) is odd, else a(n-1)/2) + (a(n-2) if a(n-2) is 
               odd, else a(n-2)/2).
%e A120424 Given a(21)=100 and a(22)=117, then a(23)=50+117=167. Given a(13)=64 
               and a(14)=68, then a(15)=32+34=66.
%t A120424 HalfFib[a_, b_, n_] := Module[{HF, i}, HF = {a, b}; For [i = 3, i < n, 
               i++, HF = Append[HF, HF[[i - 2]]/(2 - Mod[HF[[i - 2]], 2]) + HF[[i 
               - 1]]/(2 - Mod[HF[[i - 1]], 2])]]; HF] HalfFib[1,3,100]
%Y A120424 Cf. A069202.
%Y A120424 Sequence in context: A023713 A032890 A092859 this_sequence A139440 A102607 
               A079463
%Y A120424 Adjacent sequences: A120421 A120422 A120423 this_sequence A120425 A120426 
               A120427
%K A120424 easy,nonn
%O A120424 0,2
%A A120424 Reed Kelly (math(AT)keldesign.com), Jul 11 2006