A238481 Number of partitions p of n that do not include (min(p) + max(p))/2 as a part.

0, 0, 1, 2, 5, 6, 12, 16, 22, 33, 46, 57, 83, 110, 138, 188, 244, 308, 403, 513, 642, 826, 1035, 1285, 1615, 2014, 2475, 3077, 3782, 4626, 5678, 6934, 8410, 10242, 12386, 14951, 18042, 21711, 26011, 31198, 37283, 44465, 52978, 62999, 74699, 88580, 104753

Offset

1,4

Links

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

Formula

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

Example

a(6) counts these partitions:
  51 (as part (5+1)/2 = 3 is not included),
  42 (as (4+2)/2 = 3 is not included),
  411 (as (4+1)/2 = 2.5 cannot be included),
  3111 (as (3+1)/2 = 2 is not included),
  2211 (as (2+1)/2 = 1.5 cannot be included),
  21111 (ditto).
Thus a(6) = 6.

Mathematica

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

Crossrefs

Cf. A238480.

Sequence in context: A309043 A023143 A085206 * A058601 A108365 A064765

Adjacent sequences: A238478 A238479 A238480 * A238482 A238483 A238484

Keyword

nonn,easy

Author

Clark Kimberling, Feb 27 2014

Status

approved