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A160000 Number of partitions of n into parts occurring in '3x+1'-trajectory starting with n.

%I A160000 #8 Jan 28 2014 00:52:40
%S A160000 1,2,3,4,5,11,9,10,17,20,23,66,35,57,51,36,77,153,122,126,61,213,189,
%T A160000 883,353,338,337,851,645,570,571,202,1220,1066,901,4017,3462,2440,
%U A160000 2777,1598,1852,512,8084,4909,3952,3122,3399,29851,17813,11391,11285,7128
%N A160000 Number of partitions of n into parts occurring in '3x+1'-trajectory starting with n.
%H A160000 R. Zumkeller, <a href="/A160000/b160000.txt">Table of n, a(n) for n = 1..100</a>
%H A160000 Wikipedia, <a href="http://en.wikipedia.org/wiki/Collatz_conjecture">Collatz conjecture</a>
%H A160000 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A160000 7-22-11-34-17-52-26-13-40-20-10-5-16-8-[4-2-1]*:
%e A160000 {1,2,4,5,7} is the set of numbers <= n, occurring in this trajectory, therefore a(7) = #{7, 5+2, 5+1+1, 4+2+1, 4+1+1+1, 2+2+2+1, 2+2+1+1+1, 2+1+1+1+1+1, 1+1+1+1+1+1+1} = 9.
%o A160000 (Haskell)
%o A160000 a160000 n = p (takeWhile (<= n) $ sort $ a070165_row n) n where
%o A160000    p _          0 = 1
%o A160000    p []         _ = 0
%o A160000    p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
%o A160000 -- _Reinhard Zumkeller_, Sep 01 2012
%Y A160000 Cf. A160001, A000041, A159999, A006370.
%Y A160000 Cf. A070165.
%K A160000 nonn,look
%O A160000 1,2
%A A160000 _Reinhard Zumkeller_, May 11 2009