A238487 Number of partitions p of n not containing round((min(p) + max(p))/2) as a part.

0, 0, 0, 1, 2, 4, 6, 11, 14, 24, 30, 44, 57, 84, 102, 145, 180, 241, 302, 403, 494, 648, 796, 1015, 1253, 1593, 1941, 2439, 2969, 3680, 4477, 5523, 6672, 8176, 9847, 11968, 14385, 17406, 20816, 25066, 29896, 35802, 42587, 50819, 60214, 71585, 84594, 100151

Offset

1,5

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..48.

Formula

a(n) + A238486(n) = A000041(n).

Example

a(6) counts these partitions:  51, 42, 411, 3111.

Mathematica

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

Crossrefs

Cf. A238486.

Sequence in context: A274261 A156913 A238483 * A138461 A173397 A187492

Adjacent sequences: A238484 A238485 A238486 * A238488 A238489 A238490

Keyword

nonn,easy

Author

Clark Kimberling, Feb 27 2014

Status

approved