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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
OFFSET
1,3
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 11 2009
STATUS
approved