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%I #8 Oct 15 2013 22:32:24
%S 0,1,4,6,19,31,73,144,331,672,1468,3024,6065,9592,19701,39630,79625,
%T 157569,316139,632655,1264043,2532963,5060484,10128862,20270752,
%U 40575156,81134041,162268825,324627203,649177198,1298516271,2596827906
%N Number of different initial values for 3x+1 trajectories started with initial values not exceeding 2^n and in which the peak values are larger than 2^n.
%e n=4: between iv={1,2,...,16} {7,9,11,13,14,15} provides
%e peak values larger than 16, so a[4]=6.
%t c[x_]:=c[x]=(1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1);c[1]=1; fpl[x_]:=FixedPointList[c, x]; {$RecursionLimit=1000;m=0}; Table[Print[{xm-1, m}];m=0; Do[If[Greater[Max[fpl[n]], 2^xm], m=m+1], {n, 1, 2^xm}], {xm, 1, 30}]
%Y Cf. A087256, A095381, A095382, A095384.
%K nonn
%O 1,3
%A _Labos Elemer_, Jun 14 2004
%E a(22)-a(32) from _Donovan Johnson_, Feb 02 2011
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