

A160001


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


2



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
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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

7221134175226134020105168[421]*:
{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 * A179750 A091173 A101897
Adjacent sequences: A159998 A159999 A160000 * A160002 A160003 A160004


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, May 11 2009


STATUS

approved



