login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A182616 Number of partitions of 2n that contain odd parts. 1
0, 1, 3, 8, 17, 35, 66, 120, 209, 355, 585, 946, 1498, 2335, 3583, 5428, 8118, 12013, 17592, 25525, 36711, 52382, 74173, 104303, 145698, 202268, 279153, 383145, 523105, 710655, 960863, 1293314, 1733281, 2313377, 3075425, 4073085, 5374806, 7067863, 9263076 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Bisection (even part) of A086543.

LINKS

Table of n, a(n) for n=0..38.

FORMULA

a(n) = A000041(2*n) - A000041(n).

EXAMPLE

For n=3 the partitions of 2n are

6 ....................... does not contains odd parts

3 + 3 ................... contains odd parts ........... *

4 + 2 ................... does not contains odd parts

2 + 2 + 2 ............... does not contains odd parts

5 + 1 ................... contains odd parts ........... *

3 + 2 + 1 ............... contains odd parts ........... *

4 + 1 + 1 ............... contains odd parts ........... *

2 + 2 + 1 + 1 ........... contains odd parts ........... *

3 + 1 + 1 + 1 ........... contains odd parts ........... *

2 + 1 + 1 + 1 + 1 ....... contains odd parts ........... *

1 + 1 + 1 + 1 + 1 + 1 ... contains odd parts ........... *

There are 8 partitions of 2n that contain odd parts.

Also p(2n)-p(n) = p(6)-p(3) = 11-3 = 8, where p(n) is the number of partitions of n, so a(3)=8.

MAPLE

with(combinat): a:= n-> numbpart(2*n) -numbpart(n): seq(a(n), n=0..35);

CROSSREFS

Cf. A000041, A086543, A304710.

Sequence in context: A182734 A327608 A239844 * A159217 A052996 A112523

Adjacent sequences:  A182613 A182614 A182615 * A182617 A182618 A182619

KEYWORD

nonn

AUTHOR

Omar E. Pol, Dec 03 2010

EXTENSIONS

Edited by Alois P. Heinz, Dec 03 2010

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 May 7 20:36 EDT 2021. Contains 343652 sequences. (Running on oeis4.)