login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A101707 Number of partitions of n having positive odd rank (the rank of a partition is the largest part minus the number of parts). 4
0, 1, 0, 2, 1, 4, 2, 7, 6, 13, 11, 22, 22, 38, 39, 63, 69, 103, 114, 165, 189, 262, 301, 407, 475, 626, 733, 950, 1119, 1427, 1681, 2118, 2503, 3116, 3678, 4539, 5360, 6559, 7735, 9400, 11076, 13372, 15728, 18886, 22184, 26501, 31067, 36947, 43242, 51210, 59818, 70576, 82291, 96750 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n)+A101708(n)=A064173(n).

REFERENCES

George E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976.

LINKS

Table of n, a(n) for n=1..54.

FORMULA

a(n) = (A000041(n)- A000025(n))/4. - Vladeta Jovovic, Dec 14 2004

G.f.: Sum((-1)^(k+1)*x^((3*k^2+k)/2)/(1+x^k), k=1..infinity)/Product(1-x^k, k=1..infinity). - Vladeta Jovovic, Dec 20 2004

EXAMPLE

a(7)=2 because the only partitions of 7 with positive odd rank are 421 (rank=1) and 52 (rank=3).

CROSSREFS

Cf. A000041, A101708, A064173.

Cf. A101198-A101200, A101709.

Sequence in context: A254594 A280948 A079966 * A304587 A113418 A117000

Adjacent sequences:  A101704 A101705 A101706 * A101708 A101709 A101710

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Dec 12 2004

EXTENSIONS

More terms, Joerg Arndt, Oct 07 2012

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)