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

Author

Reinhard Zumkeller, May 11 2009

Keywords

• nonn
• look

Examples

			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.
		

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

Crossrefs

Cf. A160001, A000041, A159999, A006370.

Cf. A070165.

Programs

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