A160000 Number of partitions of n into parts occurring in '3x+1'-trajectory starting with n.

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

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: A325651 A345451 A345320 * A245448 A115306 A171592

Adjacent sequences: A159997 A159998 A159999 * A160001 A160002 A160003

Keyword

nonn,look

Author

Reinhard Zumkeller, May 11 2009

Status

approved