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!)
A238478 Number of partitions of n whose median is a part. 3
1, 2, 2, 4, 5, 8, 11, 17, 22, 32, 43, 59, 78, 105, 136, 181, 233, 302, 386, 496, 626, 796, 999, 1255, 1564, 1951, 2412, 2988, 3674, 4516, 5524, 6753, 8211, 9984, 12086, 14617, 17617, 21211, 25450, 30514, 36475, 43550, 51869, 61707, 73230, 86821, 102706 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..47.

FORMULA

A238478(n) + A238479(n) = A000041(n).

For all n, a(n) >= A027193(n) [Because when a partition of n has an odd number of parts, then its median is simply the part at the middle] - Antti Karttunen, Feb 27 2014

EXAMPLE

a(6) counts these partitions:  6, 411, 33, 321, 3111, 222, 21111, 111111.

MATHEMATICA

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Median[p]]], {n, 40}]

CROSSREFS

Cf. A237984, A238480.

Sequence in context: A017910 A240734 A328460 * A013979 A107458 A274142

Adjacent sequences:  A238475 A238476 A238477 * A238479 A238480 A238481

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 27 2014

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 February 20 16:30 EST 2020. Contains 332078 sequences. (Running on oeis4.)