Fibonacci-Collatz sequence

[zak seidov]

Neil, seqfans,

not yet submitted,
pending gurus' opinions,
thanks, Zak

%I A000001
%S A000001
1,2,10,6,8,7,46,160,103,790,2680,1735,13246,44944,29095,222118,753640,487879,3724558,12637312,8180935,62454742,211907032,137180887,1047263758,3553333936,2300298847,17560898350,59583591592,38572244971
%N A000001 Fibonacci-Collatz sequence
%C A000001 Case a(1)=1;a(2)=1 gives "all ones"
sequence  1,1,1,1,1,1,1 (A000012);
similarly cases a(1)=a(2)=b give "all b's" sequences
b,b,b,b,b,b.
Do all other cases  give in general increasing
sequences (not-necessarily strictly monotonic)? 
%F A000001 a(1)=1;a(2)=2; fib=a(n-1)+a(n-2); if fib is
odd then a(n)=3*fib+1 else a(n)=fib/2
%t A000001
a[1]=1;a[2]=2;a[n_]:=a[n]=(fib=a[n-1]+a[n-2];col=If[OddQ[fib],3*fib+1,fib/2]);Table[a[n],{n,30}]
%Y A000001 A000012
%O A000001 1
%K A000001 ,nonn,
%A A000001 Zak Seidov (zakseidov at yahoo.com), Sep 12
2006


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