A362548 Number of partitions of n with at least three parts larger than 1.

0, 0, 0, 0, 0, 0, 1, 2, 5, 9, 16, 25, 40, 58, 85, 119, 166, 224, 303, 399, 526, 681, 880, 1122, 1430, 1801, 2266, 2827, 3521, 4354, 5378, 6601, 8092, 9870, 12020, 14576, 17652, 21294, 25653, 30804, 36937, 44162, 52732, 62798, 74690, 88627, 105028, 124201, 146696, 172924, 203600, 239292, 280912

Offset: 0

Author

Wouter Meeussen, Apr 24 2023

Keywords

• nonn

Comments

Both following comments are empirical observations:

1) also accumulant of A119907;

2) the characters of exactly these partitions do not occur in the decomposition of the count of parts 1<=k<=n into the characters of the symmetric group of n (Elders' Theorem).

3) the complement (partitions with no more than 2 parts >1) is counted by A033638.

Links

• Eric Weisstein's World of Mathematics, Elder's Theorem

Crossrefs

Cf. A000041, A033638, A119907.

Programs

Mathematica

Table[PartitionsP[n]-(1 + Floor[n^2/4]),{n,0,30}];
Table[ Count[Partitions[n], pa_ /; Length[DeleteCases[pa, 1]] > 2] , {n,0,30}]

Python

from sympy import npartitions
def A362548(n): return npartitions(n)-1-(n**2>>2) # Chai Wah Wu, Apr 27 2023

Formula

a(n) = A000041(n) - A033638(n).