%I #14 Mar 06 2013 17:53:33
%S 1,1,1,3,3,5,8,14,20,29,40,59,87,130,196,294,439,658,985,1459,2203,
%T 3328,5001,7482,11205,16805,25220,37850,56713,85108,127728,191635
%N Number of terms k such that difference between halving and tripling steps in Collatz (3x+1) trajectory of k is n.
%e a(5) = 5 since there are only five numbers 12, 13, 20, 21, 32 such that difference between number of halving and tripling steps is 5.
%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 15; t = Table[0, {nn}]; Do[c = Collatz[n]; e = Select[c, EvenQ]; diff = 2*Length[e]  Length[c]; If[diff < nn  1, t[[diff + 2]]++], {n, 2^(nn  1)}]; t (* _T. D. Noe_, Mar 04 2013 *)
%Y Cf. A220071, A222599 (lists of numbers).
%K nonn
%O 0,4
%A _Jayanta Basu_, Mar 04 2013
%E Corrected and extended by _T. D. Noe_, Mar 06 2013
