login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117955 Number of partitions of n into exactly 2 types of odd parts. 5
0, 0, 0, 1, 1, 2, 3, 5, 4, 7, 8, 10, 11, 13, 12, 19, 18, 20, 22, 25, 24, 30, 31, 36, 33, 39, 38, 45, 45, 48, 51, 57, 54, 60, 56, 69, 67, 72, 72, 79, 78, 84, 84, 90, 87, 97, 97, 112, 99, 107, 112, 117, 115, 126, 118, 131, 134, 137, 136, 152, 143, 149, 149, 163, 152, 174, 164 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
LINKS
D. Christopher and T. Nadu, Partitions with Fixed Number of Sizes, J. Integer Seq. 15 (2015), #15.11.5.
N. Benyahia Tani, S. Bouroubi, and O. Kihel, An effective approach for integer partitions using exactly two distinct sizes of parts, Bulletin du Laboratoire 03 (2015), 18-27.
N. Benyahia Tani, S. Bouroubi, and O. Kihel, An effective approach for integer partitions using exactly two distinct sizes of parts, Elemente der Mathematik 72(2) (2017), 66-74.
FORMULA
G.f.: sum(sum(x^(2i+2j-2)/[(1-x^(2i-1))(1-x^(2j-1))], j=1..i-1), i=1..infinity).
G.f. for number of partitions of n into exactly m types of odd parts is obtained if we substitute x(i) with -Sum_{k>0}(x^(2*n-1)/(x^(2*n-1)-1))^i in the cycle index Z(S(m); x(1),x(2),..,x(m)) of the symmetric group S(m) of degree m. - Vladeta Jovovic, Sep 20 2007
EXAMPLE
a(8)=5 because we have [7,1],[5,3],[5,1,1,1],[3,3,1,1] and [3,3,1,1].
MAPLE
g:=sum(sum(x^(2*i+2*j-2)/(1-x^(2*i-1))/(1-x^(2*j-1)), j=1..i-1), i=1..40): gser:=series(g, x=0, 75): seq(coeff(gser, x^n), n=1..72);
MATHEMATICA
With[{nmax = 60}, CoefficientList[Series[Sum[Sum[x^(2*k+2*j-2)/((1-x^(2*k -1))*(1-x^(2*j-1))), {j, 1, k-1}], {k, 1, 3*nmax}], {x, 0, nmax}], x]] (* G. C. Greubel, Oct 05 2018 *)
CROSSREFS
Cf. A002133.
Sequence in context: A256996 A316668 A099424 * A074049 A326777 A193973
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Apr 05 2006
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)