A238480 Number of partitions p of n that include (min(p) + max(p))/2 as a part.

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

Offset: 1

Author

Clark Kimberling, Feb 27 2014

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Crossrefs

Cf. A238481.

Programs

Mathematica

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