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

0,8

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

Table of n, a(n) for n=0..52.

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

Formula

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

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}]

Prog

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

Crossrefs

Cf. A000041, A033638, A119907.

Sequence in context: A284917 A007979 A097701 * A225596 A211881 A056870

Adjacent sequences: A362545 A362546 A362547 * A362549 A362550 A362551

Keyword

nonn

Author

Wouter Meeussen, Apr 24 2023

Status

approved