login
This site is supported by donations 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

REFERENCES

N. BENYAHIA TANI, S. BOUROUBI, O. KIHEL, An effective approach for integer partitions using exactly two distinct sizes of parts, Bulletin du Laboratoire, 03 (2015) 18 - 27; Availaible on line at http://www.liforce.usthb.dz.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

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);

CROSSREFS

Cf. A002133.

Sequence in context: A127515 A256996 A099424 * A074049 A193973 A245057

Adjacent sequences:  A117952 A117953 A117954 * A117956 A117957 A117958

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 | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 24 16:41 EDT 2016. Contains 275781 sequences.