%I #5 Mar 30 2012 18:51:00
%S 0,0,1,0,1,1,3,1,2,1,1,2,2,4,3,1,1,3,3,1,7,2,1,3,1,2,2,5,4,3,4,1,4,2,
%T 7,5,3,2,3,5,1,9,5,2,6,3,3,4,8,4,5,5,4,6,5,8,5,3,5,7,5,5,11,5,3,7,6,4,
%U 7,10,6,4,7,6,6,6,11,6,4,7,6,5,5,14,6,3,7,8,4,7,16,5,6,6,7,5,5,12,8,3,7,7
%N Number of ways to write n as sum of initial terms of a Collatz trajectory starting with a value less than n.
%C a(n) = 0 iff A139435(n) = 0; a(n) > 0 for n > 4;
%C a(A139437(n)) = 1.
%H R. Zumkeller, <a href="/A139436/b139436.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CollatzProblem.html">Collatz Problem</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e a(10) = #{2+1+4+2+1} = 1;
%e a(11) = #{4+2+1+4} = 1;
%e a(12) = #{1+4+2+1+4,8+4} = 2;
%e a(13) = #{4+2+1+4+2,3+10} = 2;
%e a(14) = #{1+4+2+1+4+2,2+1+4+2+1+4,4+2+1+4+2+1,8+4+2} = 4;
%e a(15) = #{1+4+2+1+4+2+1,8+4+2+1,10+5} = 3.
%Y Cf. A006370.
%K nonn
%O 1,7
%A _Reinhard Zumkeller_, Apr 21 2008