A211860 Number of partitions of n into parts <= 5 with the property that all parts have distinct multiplicities.

1, 1, 2, 2, 4, 5, 6, 9, 11, 12, 16, 22, 21, 33, 37, 39, 51, 65, 63, 86, 85, 105, 118, 149, 148, 185, 198, 238, 251, 304, 304, 381, 388, 454, 478, 565, 576, 679, 704, 819, 842, 978, 1013, 1168, 1195, 1377, 1415, 1616, 1668, 1874, 1937, 2197, 2246, 2512, 2625

Offset

0,3

Links

Table of n, a(n) for n=0..54.

Doron Zeilberger, Using generatingfunctionology to enumerate distinct-multiplicity partitions.

Example

For n=3 the a(3)=2 partitions are {3} and {1,1,1}. Note that {2,1} does not count, as 1 and 2 appear with the same nonzero multiplicity.

Prog

(Haskell)
a211860 n = p 0 [] [1..5] n where
   p m ms _      0 = if m `elem` ms then 0 else 1
   p _ _  []     _ = 0
   p m ms ks'@(k:ks) x
     | x < k       = 0
     | m == 0      = p 1 ms ks' (x - k) + p 0 ms ks x
     | m `elem` ms = p (m + 1) ms ks' (x - k)
     | otherwise   = p (m + 1) ms ks' (x - k) + p 0 (m : ms) ks x
-- Reinhard Zumkeller, Dec 27 2012

Crossrefs

Cf. A026811, A098859.

Cf. A105637, A211858, A211859, A211861, A211862, A211863.

Sequence in context: A238433 A238424 A121269 * A250114 A056219 A085140

Adjacent sequences: A211857 A211858 A211859 * A211861 A211862 A211863

Keyword

nonn

Author

Matthew C. Russell, Apr 25 2012

Status

approved