|
Search: id:A027349
|
|
|
| A027349 |
|
Number of partitions of n into distinct odd parts, the least being 1. |
|
+0
5
|
|
| 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 4, 4, 5, 6, 6, 6, 8, 8, 9, 9, 11, 12, 13, 13, 16, 17, 18, 19, 22, 24, 25, 27, 30, 33, 35, 37, 41, 46, 47, 51, 56, 61, 64, 69, 75, 82, 86, 92, 100, 109, 114, 122, 133, 143, 151, 161, 174
(list; graph; listen)
|
|
|
OFFSET
|
1,13
|
|
|
COMMENT
|
Column 1 of A116860. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2006
Also number of partitions of n such that the largest part occurs exactly once and each number smaller than the largest part occurs an even nonzero number of times. Example: a(17)=3 because we have [3,2,2,2,2,2,2,1,1],[3,2,2,2,2,1,1,1,1,1,1], and [3,2,2,1,1,1,1,1,1,1,1,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 13 2006
|
|
FORMULA
|
G.f.=x*product(1+x^(2i-1), i=2..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2006
G.f.=sum(x^(k^2)/product(1-x^(2j), j=1..k-1), k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 13 2006
|
|
EXAMPLE
|
a(17)=3 because we have [13,3,1],[11,5,1], and [9,7,1].
|
|
MAPLE
|
N := 100; t1 := series(mul(1+x^(2*k+1), k=1..N), x, N); A027349 := proc(n) coeff(t1, x, n); end;
|
|
CROSSREFS
|
Cf. A116860.
Sequence in context: A026922 A008624 A059169 this_sequence A053277 A078661 A029263
Adjacent sequences: A027346 A027347 A027348 this_sequence A027350 A027351 A027352
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu)
|
|
|
Search completed in 0.002 seconds
|
