A211862 - OEIS

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A211862

Number of partitions of n into parts <= 7 with the property that all parts have distinct multiplicities.

1, 1, 2, 2, 4, 5, 7, 10, 12, 14, 19, 25, 26, 39, 46, 51, 65, 84, 87, 116, 123, 147, 171, 216, 220, 281, 306, 364, 402, 496, 511, 636, 678, 793, 861, 1032, 1062, 1273, 1360, 1569, 1683, 1978, 2054, 2428, 2566, 2953, 3118, 3627, 3812, 4378, 4631

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..50.

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)

a211862 n = p 0 [] [1..7] 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. A026813, A098859.

Cf. A105637, A211858, A211859, A211860, A211861, A211863.

Sequence in context: A135833 A137200 A026930 * A286948 A211863 A333190

Adjacent sequences: A211859 A211860 A211861 * A211863 A211864 A211865

KEYWORD

nonn

AUTHOR

Matthew C. Russell, Apr 25 2012

STATUS

approved