|
Search: id:A027336
|
|
|
| A027336 |
|
Number of partitions of n that do not contain 2 as a part. |
|
+0
9
|
|
| 1, 1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 35, 45, 58, 75, 96, 121, 154, 193, 242, 302, 375, 463, 573, 703, 861, 1052, 1282, 1555, 1886, 2277, 2745, 3301, 3961, 4740, 5667, 6754, 8038, 9548, 11323, 13398, 15836, 18678, 22001, 25873, 30383, 35620, 41715, 48771
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Also number of partitions of n into parts with at most one 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 25 2004
Also number of partitions of n into parts with at least half of the parts having size 1; equivalently (by duality) number of partitions of n where the large part is at least twice as big as the second largest part. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 08 2005
|
|
LINKS
|
P. Chinn and S. Heubach, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, 6 (2003), no. 2, Article 03.2.3.
|
|
FORMULA
|
G.f.: (1-x^2) Product_{m>0} 1/(1-x^m).
a(n)=p(n)-p(n-2) for n>=2, where p(n) are the partition numbers (A000041); follows at once from the g.f. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 18 2006
|
|
MAPLE
|
with(combinat): a:=proc(n) if n=0 then 1 elif n=1 then 1 else numbpart(n)-numbpart(n-2) fi end: seq(a(n), n=0..49); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 18 2006
|
|
PROGRAM
|
(PARI) a(n)=if(n<0, 0, polcoeff((1-x^2)/eta(x+x*O(x^n)), n))
|
|
CROSSREFS
|
Cf. A027337.
Pairwise sums of sequence A002865 (partitions in which the least part is at least 2).
a(n)=A000041(n)-A000041(n-2).
Sequence in context: A035980 A035990 A036001 this_sequence A023434 A087192 A046935
Adjacent sequences: A027333 A027334 A027335 this_sequence A027337 A027338 A027339
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu)
|
|
EXTENSIONS
|
More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 10 2002
|
|
|
Search completed in 0.002 seconds
|
