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

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, 10, 1, 40, 19, 8, 138, 90, 55, 62, 7, 17, 3, 144, 63, 34, 16, 16, 43, 218, 148, 105, 22, 7, 39, 24, 323, 371, 150, 224, 54, 27, 40, 30, 1, 572, 444, 344, 71, 32, 19, 39, 1766, 52

Offset: 1

Author

Reinhard Zumkeller, May 11 2009

Keywords

• nonn

Examples

			7-22-11-34-17-52-26-13-40-20-10-5-16-8-[4-2-1]*:
{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.
		

Links

• R. Zumkeller, Table of n, a(n) for n = 1..100
• Wikipedia, Collatz conjecture
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A160000, A000009, A159999, A006370.

Cf. A070165.

Programs

Haskell

a160001 n = p (takeWhile (<= n) $ sort $ a070165_row n) n where
   p _      0 = 1
   p []     _ = 0
   p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
-- Reinhard Zumkeller, Sep 01 2012