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A160000 Number of partitions of n into parts occurring in '3x+1'-trajectory starting with n. 2
1, 2, 3, 4, 5, 11, 9, 10, 17, 20, 23, 66, 35, 57, 51, 36, 77, 153, 122, 126, 61, 213, 189, 883, 353, 338, 337, 851, 645, 570, 571, 202, 1220, 1066, 901, 4017, 3462, 2440, 2777, 1598, 1852, 512, 8084, 4909, 3952, 3122, 3399, 29851, 17813, 11391, 11285, 7128 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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, 5+1+1, 4+2+1, 4+1+1+1, 2+2+2+1, 2+2+1+1+1, 2+1+1+1+1+1, 1+1+1+1+1+1+1} = 9.

PROG

(Haskell)

a160000 n = p (takeWhile (<= n) $ sort $ a070165_row n) n where

   p _          0 = 1

   p []         _ = 0

   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m

-- Reinhard Zumkeller, Sep 01 2012

CROSSREFS

Cf. A160001, A000041, A159999, A006370.

Cf. A070165.

Sequence in context: A111666 A080475 A247233 * A245448 A115306 A171592

Adjacent sequences:  A159997 A159998 A159999 * A160001 A160002 A160003

KEYWORD

nonn,look

AUTHOR

Reinhard Zumkeller, May 11 2009

STATUS

approved

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Last modified September 20 15:44 EDT 2017. Contains 292275 sequences.