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

1,3

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

Example

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.

Prog

(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

Crossrefs

Cf. A160000, A000009, A159999, A006370.

Cf. A070165.

Sequence in context: A256184 A120855 A193737 * A339549 A179750 A091173

Adjacent sequences: A159998 A159999 A160000 * A160002 A160003 A160004

Keyword

nonn

Author

Reinhard Zumkeller, May 11 2009

Status

approved