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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 (list; graph; refs; listen; history; text; internal format)
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 * A179750 A091173 A101897

Adjacent sequences:  A159998 A159999 A160000 * A160002 A160003 A160004

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 11 2009

STATUS

approved

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Last modified February 18 17:08 EST 2018. Contains 299325 sequences. (Running on oeis4.)