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A211859 Number of partitions of n into parts <= 4 with the property that all parts have distinct multiplicities. 7
1, 1, 2, 2, 4, 4, 6, 8, 10, 10, 14, 18, 18, 26, 31, 30, 39, 48, 48, 61, 63, 73, 84, 101, 98, 124, 132, 147, 156, 188, 182, 223, 227, 257, 272, 322, 306, 367, 377, 417, 427, 499, 488, 564, 567, 645, 647, 740, 720, 828, 836, 920, 924, 1048, 1030, 1173, 1161 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f.: (9*x^45 +20*x^44 +44*x^43 +76*x^42 +121*x^41 +172*x^40 +234*x^39 +292*x^38 +346*x^37 +380*x^36 +412*x^35 +415*x^34 +417*x^33 +401*x^32 +389*x^31 +365*x^30 +361*x^29 +351*x^28 +359*x^27 +365*x^26 +383*x^25 +391*x^24 +413*x^23 +422*x^22 +436*x^21 +444*x^20 +454*x^19 +454*x^18 +458*x^17 +450*x^16 +437*x^15 +415*x^14 +383*x^13 +342*x^12 +298*x^11 +248*x^10 +198*x^9 +152*x^8 +110*x^7 +76*x^6 +49*x^5 +30*x^4 +16*x^3 +8*x^2 +3*x +1) / ((x^2-x+1) *(x^4-x^3+x^2-x+1) *(x^6+x^3+1) *(x^4+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(x^2+x+1)^2 *(x^4+x^3+x^2+x+1)^2 *(x^2+1)^2 *(x+1)^3 *(x-1)^4). - Alois P. Heinz, Feb 09 2017

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)

a211859 n = p 0 [] [1..4] 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. A026810, A098859.

Cf. A105637, A211858, A211860, A211861, A211862, A211863.

Sequence in context: A218897 A218064 A183002 * A057601 A294150 A087135

Adjacent sequences:  A211856 A211857 A211858 * A211860 A211861 A211862

KEYWORD

nonn,easy

AUTHOR

Matthew C. Russell, Apr 25 2012

STATUS

approved

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Last modified November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)