A238486 Number of partitions p of n containing round((min(p) + max(p))/2) as a part.

1, 2, 3, 4, 5, 7, 9, 11, 16, 18, 26, 33, 44, 51, 74, 86, 117, 144, 188, 224, 298, 354, 459, 560, 705, 843, 1069, 1279, 1596, 1924, 2365, 2826, 3471, 4134, 5036, 6009, 7252, 8609, 10369, 12272, 14687, 17372, 20674, 24356, 28920, 33973, 40160, 47122, 55471

Offset

1,2

Comments

As used here, if k is a positive integer, then round(k + 1/2) = k + 1.

Links

Table of n, a(n) for n=1..49.

Formula

a(n) + A238487(n) = A000041(n).

Example

a(6) counts these partitions:  6, 33, 321, 222, 2211, 21111, 111111.

Mathematica

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Round[(Min[p] + Max[p])/2]]], {n, 30}]

Crossrefs

Cf. A238487.

Sequence in context: A291927 A239497 A039850 * A238482 A368483 A033100

Adjacent sequences: A238483 A238484 A238485 * A238487 A238488 A238489

Keyword

nonn,easy

Author

Clark Kimberling, Feb 27 2014

Status

approved