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A160001 Number of partitions of n into distinct parts occurring in '3x+1'-trajectory starting with n.

%I A160001 #6 Sep 01 2012 13:59:58
%S A160001 1,1,2,1,2,4,3,1,4,3,4,9,4,8,5,1,6,18,10,5,2,13,6,25,19,10,8,41,24,14,
%T A160001 10,1,40,19,8,138,90,55,62,7,17,3,144,63,34,16,16,43,218,148,105,22,7,
%U A160001 39,24,323,371,150,224,54,27,40,30,1,572,444,344,71,32,19,39,1766,52
%N A160001 Number of partitions of n into distinct parts occurring in '3x+1'-trajectory starting with n.
%H A160001 R. Zumkeller, <a href="/A160001/b160001.txt">Table of n, a(n) for n = 1..100</a>
%H A160001 Wikipedia, <a href="http://en.wikipedia.org/wiki/Collatz_conjecture">Collatz conjecture</a>
%H A160001 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A160001 7-22-11-34-17-52-26-13-40-20-10-5-16-8-[4-2-1]*:
%e A160001 {1,2,4,5,7} is the set of numbers <= n, occurring in this trajectory, therefore a(7) = #{7, 5+2, 4+2+1} = 3.
%o A160001 (Haskell)
%o A160001 a160001 n = p (takeWhile (<= n) $ sort $ a070165_row n) n where
%o A160001    p _      0 = 1
%o A160001    p []     _ = 0
%o A160001    p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
%o A160001 -- _Reinhard Zumkeller_, Sep 01 2012
%Y A160001 Cf. A160000, A000009, A159999, A006370.
%Y A160001 Cf. A070165.
%K A160001 nonn
%O A160001 1,3
%A A160001 _Reinhard Zumkeller_, May 11 2009