A238488 Number of partitions of n not containing 2*(number of parts) as a part.

1, 1, 3, 5, 6, 10, 14, 20, 28, 39, 52, 72, 95, 126, 166, 218, 280, 364, 465, 594, 753, 953, 1195, 1502, 1870, 2326, 2880, 3560, 4374, 5374, 6569, 8018, 9752, 11842, 14327, 17317, 20858, 25088, 30098, 36054, 43073, 51399, 61186, 72737, 86292, 102235, 120882

Offset

1,3

Comments

Number of z-classes in symmetric group on n points. [Bhunia et al., Cor. 1.2]. - Eric M. Schmidt, Nov 02 2017

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

Sushil Bhunia, Dilpreet Kaur, Anupam Singh, z-Classes and Rational Conjugacy Classes in Alternating Groups, arXiv:1705.06651 [math.GR], 2017.

Formula

a(n) = A000041(n) - A008483(n-2), n > 2. [Corrected by Eric M. Schmidt, Nov 02 2017]

Example

a(9) counts all the 30 partitions of 9 except 621 and 54.

Mathematica

Table[Count[IntegerPartitions[n], p_ /; ! MemberQ[p, 2*Length[p]]], {n, 40}]

Prog

(Sage) def a(n) : return 1 if n in [1, 2] else Partitions(n).cardinality() - sage.combinat.partition.Partitions_parts_in(n-2, [3..n-2]).cardinality() # Eric M. Schmidt, Nov 02 2017

Crossrefs

Cf. A008483.

Sequence in context: A190721 A112926 A176747 * A230124 A027627 A194466

Adjacent sequences: A238485 A238486 A238487 * A238489 A238490 A238491

Keyword

nonn,easy

Author

Clark Kimberling, Feb 27 2014

Status

approved