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A238480 Number of partitions p of n that include (min(p) + max(p))/2 as a part. 4
1, 2, 2, 3, 2, 5, 3, 6, 8, 9, 10, 20, 18, 25, 38, 43, 53, 77, 87, 114, 150, 176, 220, 290, 343, 422, 535, 641, 783, 978, 1164, 1415, 1733, 2068, 2497, 3026, 3595, 4304, 5174, 6140, 7300, 8709, 10283, 12176, 14435, 16978, 20001, 23579, 27640, 32423, 38024 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A238480(n) + A238481(n) = A000041(n).

LINKS

Table of n, a(n) for n=1..51.

EXAMPLE

a(6) counts these partitions:

  6 (as (6+6)/2 = 6 is included),

  33 (as (3+3)/2 = 3 is included),

  321 (as (3+1)/2 = 2 is included),

  222 (as (2+2)/2 = 2 is included),

  111111 (as (1+1)/2 = 1 is included).

Thus a(6) = 5.

MATHEMATICA

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, (Min[p] + Max[p])/2]], {n, 40}]

CROSSREFS

Cf. A238481.

Sequence in context: A151663 A162753 A307994 * A111089 A051664 A318884

Adjacent sequences:  A238477 A238478 A238479 * A238481 A238482 A238483

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 27 2014

STATUS

approved

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Last modified November 29 23:37 EST 2020. Contains 338780 sequences. (Running on oeis4.)